PSI_Assignment 1: Digital Portfolio: Modelling Part
Na Li (D19125334)
knitr::opts_chunk$set(echo = FALSE)
needed_packages <- c("VIM", "tidyverse","pastecs", "ggplot2", "semTools", "psych", "FSA", "car", "effectsize", "coin", "rstatix", "sjstats", "userfriendlyscience", "stats", "foreign", "gmodels", "lm.beta","stargazer", "lmtest", "DescTools", "nnet", "reshape2", "generalhoslem", "Epi", "arm", "regclass", "olsrr","REdaS", "Hmisc","corrplot","ggcorrplot", "factoextra", "nFactors")
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library(pastecs) #For creating descriptive statistic summaries
library(ggplot2) #For creating histograms with more detail than plot
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#Multinomial regression
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## parallel#getwd()
stdMathData=read.table("student-mat.csv",sep=";",header=TRUE)
stdPorlagData=read.table("student-por.csv",sep=";",header=TRUE)
stdMergeData=merge(stdMathData,stdPorlagData,by=c("school","sex","age","address","famsize","Pstatus","Medu","Fedu","Mjob","Fjob","reason","nursery","internet"))
colnames(stdMathData) <- tolower(colnames(stdMathData))
colnames(stdPorlagData) <- tolower(colnames(stdPorlagData))
colnames(stdMergeData) <- tolower(colnames(stdMergeData))Linear Regression
Build Linear Regression Model
#G1 and G2 for math course with paid (yes, no)
# G2 is predicted by g1 including dummy variable for paid that extra paid classes within the Math course to investigate a differential effect by paid.
# Descriptives and visuals for g1 (first period grade)
gg_g1 <- ggplot(stdMathData, aes(x=g1)) +
labs(x="Normalised first period grade (g1)") +
ggtitle("Figure 1 - Histogram for Normalised first period grade of Math") +
geom_histogram(binwidth=2, colour="black", aes(y=..density.., fill=..count..)) +
scale_fill_gradient("Count", low="#DCDCDC", high="#7C7C7C") +
stat_function(fun=dnorm, color="red",args=list(mean=mean(stdMathData$g1, na.rm=TRUE), sd=sd(stdMathData$g1, na.rm=TRUE)))
gg_g1
qqnorm(stdMathData$g1, main="Figure 2 - QQ Plot for Normalised First period grade of Math")
qqline(stdMathData$g1, col=2)
# statistics descpritve
#g1 generae summary statistics
pastecs::stat.desc(stdMathData$g1, basic=F)## median mean SE.mean CI.mean.0.95 var std.dev
## 11.0000000 10.9088608 0.1670068 0.3283359 11.0170533 3.3191947
## coef.var
## 0.3042659#skewness and kurtosis
tpskew <- semTools::skew(stdMathData$g1)
tpkurt <- semTools::kurtosis(stdMathData$g1)
tpskew[1]/tpskew[2]## skew (g1)
## 1.952282tpkurt[1]/tpkurt[2]## Excess Kur (g2)
## -2.814788mathg1<- abs(scale(stdMathData$g1))
FSA::perc(as.numeric(mathg1), 1.96, "gt")## [1] 3.291139FSA::perc(as.numeric(mathg1), 3.29, "gt")## [1] 0length(stdMathData$g1)## [1] 395# Descriptives and visuals for g2 (second period grade) ---- predicted
gg_g2 <- ggplot(stdMathData, aes(x=g2)) +
labs(x="Normalised Second period grade") +
ggtitle("Figure 3 - Histogram for Normalised second period grade of Math") +
geom_histogram(binwidth=2, colour="black", aes(y=..density.., fill=..count..)) +
scale_fill_gradient("Count", low="#DCDCDC", high="#7C7C7C") +
stat_function(fun=dnorm, color="red",args=list(mean=mean(stdMathData$g2, na.rm=TRUE), sd=sd(stdMathData$g2, na.rm=TRUE)))
gg_g2
qqnorm(stdMathData$g2, main="Figure 4 - QQ Plot for Normalised second period grade of Math")
qqline(stdMathData$g2, col=2)
# statistics descpritve
#g2 generate summary statistics
pastecs::stat.desc(stdMathData$g2, basic=F)## median mean SE.mean CI.mean.0.95 var std.dev
## 11.0000000 10.7139241 0.1892618 0.3720894 14.1489173 3.7615047
## coef.var
## 0.3510856#skewness and kurtosis
tpskew <- semTools::skew(stdMathData$g2)
tpkurt <- semTools::kurtosis(stdMathData$g2)
tpskew[1]/tpskew[2]## skew (g1)
## -3.502273tpkurt[1]/tpkurt[2]## Excess Kur (g2)
## 2.546531mathg2<- abs(scale(stdMathData$g2))
FSA::perc(as.numeric(mathg2), 1.96, "gt")## [1] 4.050633FSA::perc(as.numeric(mathg2), 3.29, "gt")## [1] 0length(stdMathData$g2)## [1] 395# Explore relationship between g1 and g2
#show scatterplot of second period grade (g2) (y) and the first period grade (g1) (x)
scat_g2g1 <- ggplot2::ggplot(stdMathData, aes(g1, g2))
#Add a regression line
scat_g2g1 + geom_point() + geom_smooth(method = "lm", colour = "Red", se = F) + labs(x = "1st Period Grade for Math course", y = "Normalised 2nd Period Grade for Math course") ## `geom_smooth()` using formula 'y ~ x'
#Pearson Correlation
stats::cor.test(stdMathData$g1, stdMathData$g2, method='pearson')##
## Pearson's product-moment correlation
##
## data: stdMathData$g1 and stdMathData$g2
## t = 32.278, df = 393, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.8226117 0.8770475
## sample estimates:
## cor
## 0.8521181# simple linear regression -> g2 predicted by g1
model_g1g2 <- lm(stdMathData$g2 ~ stdMathData$g1)
anova(model_g1g2)## Analysis of Variance Table
##
## Response: stdMathData$g2
## Df Sum Sq Mean Sq F value Pr(>F)
## stdMathData$g1 1 4047.8 4047.8 1041.9 < 2.2e-16 ***
## Residuals 393 1526.9 3.9
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("\n *******Summary Model_g1g2*******\n") ##
## *******Summary Model_g1g2*******summary(model_g1g2)##
## Call:
## lm(formula = stdMathData$g2 ~ stdMathData$g1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.7676 -0.8363 0.1637 1.1637 4.1981
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.17957 0.34110 0.526 0.599
## stdMathData$g1 0.96567 0.02992 32.278 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.971 on 393 degrees of freedom
## Multiple R-squared: 0.7261, Adjusted R-squared: 0.7254
## F-statistic: 1042 on 1 and 393 DF, p-value: < 2.2e-16lm.beta::lm.beta(model_g1g2)##
## Call:
## lm(formula = stdMathData$g2 ~ stdMathData$g1)
##
## Standardized Coefficients::
## (Intercept) stdMathData$g1
## 0.0000000 0.8521181stargazer(model_g1g2, type="text") #Tidy output of all the required stats##
## ===============================================
## Dependent variable:
## ---------------------------
## g2
## -----------------------------------------------
## g1 0.966***
## (0.030)
##
## Constant 0.180
## (0.341)
##
## -----------------------------------------------
## Observations 395
## R2 0.726
## Adjusted R2 0.725
## Residual Std. Error 1.971 (df = 393)
## F Statistic 1,041.857*** (df = 1; 393)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01# add paid: extra paid classes within the course subject (Math or Portuguese) (binary: yes or no)
# paid as dummy variable
model_g1g2p <- lm(stdMathData$g2 ~ stdMathData$g1 + stdMathData$paid)
anova(model_g1g2p)## Analysis of Variance Table
##
## Response: stdMathData$g2
## Df Sum Sq Mean Sq F value Pr(>F)
## stdMathData$g1 1 4047.8 4047.8 1059.2284 < 2e-16 ***
## stdMathData$paid 1 28.9 28.9 7.5525 0.00627 **
## Residuals 392 1498.0 3.8
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("\n *******Summary Model_g1g2p*******\n") ##
## *******Summary Model_g1g2p*******summary(model_g1g2p)##
## Call:
## lm(formula = stdMathData$g2 ~ stdMathData$g1 + stdMathData$paid)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.5153 -0.7405 0.0168 0.9605 4.4471
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.03443 0.34714 -0.099 0.92104
## stdMathData$g1 0.96248 0.02969 32.414 < 2e-16 ***
## stdMathData$paidyes 0.54293 0.19756 2.748 0.00627 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.955 on 392 degrees of freedom
## Multiple R-squared: 0.7313, Adjusted R-squared: 0.7299
## F-statistic: 533.4 on 2 and 392 DF, p-value: < 2.2e-16lm.beta::lm.beta(model_g1g2p)##
## Call:
## lm(formula = stdMathData$g2 ~ stdMathData$g1 + stdMathData$paid)
##
## Standardized Coefficients::
## (Intercept) stdMathData$g1 stdMathData$paidyes
## 0.00000000 0.84930404 0.07200818stargazer(model_g1g2p, type="text")##
## ===============================================
## Dependent variable:
## ---------------------------
## g2
## -----------------------------------------------
## g1 0.962***
## (0.030)
##
## paidyes 0.543***
## (0.198)
##
## Constant -0.034
## (0.347)
##
## -----------------------------------------------
## Observations 395
## R2 0.731
## Adjusted R2 0.730
## Residual Std. Error 1.955 (df = 392)
## F Statistic 533.390*** (df = 2; 392)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01Linear Model Assumptions
#Influential Outliers - Cook's distance
cooksd_modelg1g2p<-sort(cooks.distance(model_g1g2p))
# plot Cook's distance
plot(cooksd_modelg1g2p, pch="*", cex=2, main="Influential Observations by Cooks distance")
abline(h = 4*mean(cooksd_modelg1g2p, na.rm=T), col="red") # add cutoff line
# add labels
text(x=1:length(cooksd_modelg1g2p)+1, y=cooksd_modelg1g2p, labels=ifelse(cooksd_modelg1g2p>4*mean(cooksd_modelg1g2p, na.rm=T),names(cooksd_modelg1g2p),""), col="blue") 
influential <- as.numeric(names(cooksd_modelg1g2p)[(cooksd_modelg1g2p > 4*mean(cooksd_modelg1g2p, na.rm=T))]) # influential row numbers
stem(influential)##
## The decimal point is 2 digit(s) to the right of the |
##
## 0 | 1
## 1 | 334444556667
## 2 | 4567
## 3 | 3head(stdMathData[influential, ]) # influential observations.## school sex age address famsize pstatus medu fedu mjob fjob reason
## 255 GP M 17 R GT3 T 2 1 other other course
## 157 GP M 17 R LE3 T 1 2 other other reputation
## 165 GP M 17 R LE3 T 1 1 other services course
## 5 GP F 16 U GT3 T 3 3 other other home
## 162 GP M 15 R GT3 T 3 2 other other course
## 138 GP F 16 U GT3 A 3 3 other other course
## guardian traveltime studytime failures schoolsup famsup paid activities
## 255 mother 1 1 0 no no no no
## 157 mother 1 1 0 no no no no
## 165 mother 4 2 3 no no no yes
## 5 father 1 2 0 no yes yes no
## 162 mother 2 2 2 yes yes no no
## 138 other 2 1 2 no yes no yes
## nursery higher internet romantic famrel freetime goout dalc walc health
## 255 no yes yes no 4 4 2 2 4 5
## 157 yes yes no no 2 2 2 3 3 5
## 165 yes no no yes 5 3 5 1 5 5
## 5 yes yes no no 4 3 2 1 2 5
## 162 yes yes yes yes 4 4 4 1 4 3
## 138 no yes yes yes 4 3 2 1 1 5
## absences g1 g2 g3
## 255 0 8 12 12
## 157 8 16 12 13
## 165 0 5 8 7
## 5 4 6 10 10
## 162 6 5 9 7
## 138 0 4 0 0cat("\n *******influential observations - the values of g1*******\n") ##
## *******influential observations - the values of g1*******head(stdMathData[influential, ]$g1)## [1] 8 16 5 6 5 4cat("\n *******influential observations - the values of g2*******\n") ##
## *******influential observations - the values of g2*******head(stdMathData[influential, ]$g2)## [1] 12 12 8 10 9 0cat("\n *******influential observations - the values of paid*******\n") ##
## *******influential observations - the values of paid*******head(stdMathData[influential, ]$paid)## [1] "no" "no" "no" "yes" "no" "no"car::outlierTest(model_g1g2p) # Bonferonni p-value for most extreme obs, looking for any cases where the outcome variable has an unusual variable for its predictor values.## rstudent unadjusted p-value Bonferroni p
## 131 -6.179178 1.6196e-09 6.3973e-07
## 136 -5.617932 3.6756e-08 1.4519e-05
## 137 -5.070408 6.1409e-07 2.4257e-04
## 135 -4.534650 7.6834e-06 3.0349e-03
## 132 -4.008873 7.3075e-05 2.8865e-02car::leveragePlots(model_g1g2p) # leverage plots
plot(model_g1g2p, 1)
plot(model_g1g2p, 3)
The first plot is the chart of residuals vs fitted values, in the second plot the standardised residuals are on the Y axis. If there is absolutely no heteroscedastity, you should see a completely random, equal distribution of points throughout the range of X axis and a flat red line. I expect to see that there is no pattern in the residuals and that they are equally spread around the y = 0 line - the dashed line.
in this case, as the red line is slightly distorted in the middle on first plot but is not a big problem. Looking at the second plot we can see that while it is a problem it is not huge. Only a concern if there are definite patterns.#Create histogram and density plot of the residuals
plot(density(resid(model_g1g2p))) 
#Create a QQ plotqqPlot(model, main="QQ Plot") #qq plot for Standardised residuals
car::qqPlot(model_g1g2p, main="QQ Plot")
## [1] 131 136##
## ****** Calculate Collinearity ******## stdMathData$g1 stdMathData$paid
## 1.00153 1.00153##
## ****** Calculate tolerance ******## stdMathData$g1 stdMathData$paid
## 0.9984728 0.9984728Report Linear Model:
A multiple regression was carried out to investigate whether first period grades of Math course and extra paid classes within the course subject could significantly predict participants’ second period grades. second period grades of the histogram, normal QQ plot of standardised residuals and the scatterplot of the dependent variable, second period grades and the standardised residuals showed that the some outliers existed.
However, second period grades of the standardised residuals showed that could be considered to have undue influence (95% within limits of -1.96 to plus 1.96 and with Cook’s distance >1 as outlined in Field (2013).
The scatterplot of standardised residuals showed that the data met the assumptions of homogeneity of variance and linearity. Examination for multicollinearity showed that the tolerance and variance influence factor measures were within acceptable levels (tolerance >0.4, VIF <2.5 ) as outlined in Tarling (2008).
The data also meets the assumption of non-zero variances of the predictors.
The results of the regression indicated that the model explained 72.99% of the variance and that the model was a significant predictor of the second period grades, F(2,26) = 533.4, p < 0.001. While the first period grades contributed significantly to the model (B = 0.962, p<0.001), the extra paid classes contributed significantly to the model as well (B = 0.543, p < 0.05). The final predictive model was: second period grades of Math = -0.034 + (0.962*first period grades) + (0.543*extra paid classes)
Logistic Regression
#age, higher -> studytime
# age 15 ~ 22
# higher: wants to take higher education (binary: yes or no)
# studytime: weekly study time (numeric: 1 - <2 hours, 2 - 2 to 5 hours, 3 - 5 to 10 hours, or 4 - >10 hours)
cat("\n *******table: higher/studytime*******\n") ##
## *******table: higher/studytime*******with(stdPorlagData, table(higher, studytime))## studytime
## higher 1 2 3 4
## no 44 19 4 2
## yes 168 286 93 33cat("\n *******age, studytime*******\n") ##
## *******age, studytime*******with(stdPorlagData, do.call(rbind, tapply(age, studytime, function(x) c(M=mean(x), SD=sd(x)))))## M SD
## 1 16.71226 1.245747
## 2 16.76066 1.185893
## 3 16.90722 1.233917
## 4 16.34286 1.235334#Because studytime has four levels we need to indicate which level is a reference
#be comparing the other types of studytime to 2 (2-5 hours)
stdPorlagData$studytime2 <- relevel(as.factor(stdPorlagData$studytime), ref="2")
#create the model using multinom
model_multilog<-multinom(studytime2~higher+age, data = stdPorlagData,model = TRUE)## # weights: 16 (9 variable)
## initial value 899.705040
## iter 10 value 732.769569
## final value 732.369835
## convergedcat("\n *******Summary Model*******\n") ##
## *******Summary Model*******summary(model_multilog)## Call:
## multinom(formula = studytime2 ~ higher + age, data = stdPorlagData,
## model = TRUE)
##
## Coefficients:
## (Intercept) higheryes age
## 1 3.627297 -1.5501634 -0.1573233
## 3 -3.787012 0.5839930 0.1239967
## 4 3.422724 -0.2631457 -0.3227391
##
## Std. Errors:
## (Intercept) higheryes age
## 1 1.437248 0.3076346 0.07941404
## 3 1.866860 0.5763750 0.09888405
## 4 2.939262 0.7864808 0.16372365
##
## Residual Deviance: 1464.74
## AIC: 1482.74#multinom package does not include p-value calculation for the regression coefficients,
#calculate p-values using Wald tests (here z-tests).
cat("\n *******z-tests*******\n") ##
## *******z-tests*******z <- summary(model_multilog)$coefficients/summary(model_multilog)$standard.errors
z## (Intercept) higheryes age
## 1 2.523779 -5.0389762 -1.981052
## 3 -2.028546 1.0132171 1.253961
## 4 1.164484 -0.3345863 -1.971243cat("\n *******p-value*******\n") ##
## *******p-value*******pvalue <- (1 - pnorm(abs(z), 0, 1)) * 2
pvalue## (Intercept) higheryes age
## 1 0.01161008 4.680288e-07 0.04758548
## 3 0.04250451 3.109565e-01 0.20985619
## 4 0.24422785 7.379372e-01 0.04869608cat("\n *******Chi-square plus significance*******\n") ##
## *******Chi-square plus significance*******lmtest::lrtest(model_multilog)## # weights: 8 (3 variable)
## initial value 899.705040
## final value 754.080307
## converged## Likelihood ratio test
##
## Model 1: studytime2 ~ higher + age
## Model 2: studytime2 ~ 1
## #Df LogLik Df Chisq Pr(>Chisq)
## 1 9 -732.37
## 2 3 -754.08 -6 43.421 9.628e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("\n *******Pseudo Rsquared*******\n") ##
## *******Pseudo Rsquared*******DescTools::PseudoR2(model_multilog, which="CoxSnell")## CoxSnell
## 0.06471537DescTools::PseudoR2(model_multilog, which="Nagelkerke")## Nagelkerke
## 0.07173848cat("\n *******Collinearity VIF*******\n")##
## *******Collinearity VIF*******# It is however sensitive to high correlation between predictor variables (multicollinearity)
vifmodel<-car::vif(model_multilog) # GVIF^(1/(2*Df)) is the value of interest## Warning in vif.default(model_multilog): No intercept: vifs may not be sensible.vifmodel## higher age
## 11.21731 237.02501cat("\n *******Tolerance*******\n")##
## *******Tolerance*******1/vifmodel## higher age
## 0.089147968 0.004218964cat("\n *******the sensitivity, specificity, and ROC plot*******\n")##
## *******the sensitivity, specificity, and ROC plot*******Epi::ROC(form=stdPorlagData$studytime2 ~ stdPorlagData$higher+stdPorlagData$age, plot="ROC")
cat("\n *******Summary of the model with co-efficients*******\n")##
## *******Summary of the model with co-efficients*******stargazer(model_multilog, type="text")##
## ===============================================
## Dependent variable:
## -----------------------------
## 1 3 4
## (1) (2) (3)
## -----------------------------------------------
## higheryes -1.550*** 0.584 -0.263
## (0.308) (0.576) (0.786)
##
## age -0.157** 0.124 -0.323**
## (0.079) (0.099) (0.164)
##
## Constant 3.627** -3.787** 3.423
## (1.437) (1.867) (2.939)
##
## -----------------------------------------------
## Akaike Inf. Crit. 1,482.740 1,482.740 1,482.740
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01cat("\n *******Exponentiate the coefficients*******\n")##
## *******Exponentiate the coefficients*******exp(coefficients(model_multilog))## (Intercept) higheryes age
## 1 37.61102793 0.2122133 0.8544278
## 3 0.02266322 1.7931844 1.1320122
## 4 30.65279715 0.7686299 0.7241628cat("\n ****** odds ratios and 95% CI *******\n") ##
## ****** odds ratios and 95% CI *******# Odds ratios are used to calculate probabilities in a regression
# OR > 1: Predictor up, Probability of outcome occurring up.
# OR < 1: Predictor down, Probability of outcome occurring down.
cbind(Estimate=round(coef(model_multilog),4), OR=round(exp(coef(model_multilog)),4))## (Intercept) higheryes age (Intercept) higheryes age
## 1 3.6273 -1.5502 -0.1573 37.6110 0.2122 0.8544
## 3 -3.7870 0.5840 0.1240 0.0227 1.7932 1.1320
## 4 3.4227 -0.2631 -0.3227 30.6528 0.7686 0.7242#Check the assumption of linearity of independent variables and log odds using a Hosmer-Lemeshow test
generalhoslem::logitgof(stdPorlagData$studytime2, fitted(model_multilog))## Warning in generalhoslem::logitgof(stdPorlagData$studytime2,
## fitted(model_multilog)): At least one cell in the expected frequencies table is
## < 1. Chi-square approximation may be incorrect.## Warning in generalhoslem::logitgof(stdPorlagData$studytime2,
## fitted(model_multilog)): Not possible to compute 10 rows. There might be too few
## observations.##
## Hosmer and Lemeshow test (multinomial model)
##
## data: stdPorlagData$studytime2, fitted(model_multilog)
## X-squared = 5.4193, df = 12, p-value = 0.9425#calculate predicted probabilities for each of outcome levels using the fitted function
pp <- fitted(model_multilog)
dses <- data.frame(higher = c("yes", "no"), age = mean(stdPorlagData$age))
#look at the averaged predicted probabilities for different values of the continuous predictor variable write within each level of paid
dwrite_age <- data.frame(higher = rep(c("yes", "no")), age = rep(c(15:22),3))
## store the predicted probabilities for each value of age and paid
pp.write_agepaid <- cbind(dwrite_age, predict(model_multilog, newdata = dwrite_age, type = "probs", se = TRUE))
## calculate the mean probabilities within each level of age
by(pp.write_agepaid[, 3:5], pp.write_agepaid$higher, colMeans)## pp.write_agepaid$higher: no
## 2 1 3
## 0.31126795 0.58417784 0.08142109
## ------------------------------------------------------------
## pp.write_agepaid$higher: yes
## 2 1 3
## 0.5063031 0.2476073 0.2022550lpp <- reshape2::melt(pp.write_agepaid, id.vars = c("higher", "age"), value.name = "probability")
head(lpp) # view first few rows## higher age variable probability
## 1 yes 15 2 0.4543656
## 2 no 16 2 0.2285790
## 3 yes 17 2 0.5044479
## 4 no 18 2 0.2842026
## 5 yes 19 2 0.5314745
## 6 no 20 2 0.3405711## plot predicted probabilities across write values for each level of age
ggplot(lpp, aes(x = age, y = probability, colour = higher)) + geom_line() + facet_grid(variable ~
., scales = "free")
Report of Logistic regression:
A multinomial logistic regression analysis was conducted with weekly study time for Portuguese course as the outcome variable (1 - <2 hours, 2 - 2 to 5 hours, 3 - 5 to 10 hours, or 4 - >10 hours) with student age (15-22), and want to take higher education as predictors.
The data met the assumption for independent observations. Examination for multicollinearity showed that the tolerance and variance influence factor measures were not within acceptable levels (tolerance >0.4, VIF <2.5 ) as outlined in Tarling (2008). The Hosmer Lemeshow goodness of fit statistic did not indicate any issues with the assumption of linearity between the independent variables and the log odds of the model (χ2(n=12) =11.09, p =0.9).Dimension Reduction
dataset from 50 items, for this dimension reduction, I selected three factors: agreebleness, extraversion and openness
std = read.table("studentpIusepersonality.csv",sep=",",header=TRUE)
std_quest <- std[, -(1:54)]
# subset dataset only keep the IPIP Big-Five 50 item
cols_A = paste0("A", c(1,2,3,4,5,6,7,8,9,10)) #agreeableness
cols_E = paste0("E", c(1,2,3,4,5,6,7,8,9,10)) #Extraversion
cols_C = paste0("C", c(1,2,3,4,5,6,7,8,9,10)) #Conscientiousness
cols_N = paste0("N", c(1,2,3,4,5,6,7,8,9,10)) #Neuroticism
cols_O = paste0("O", c(1,2,3,4,5,6,7,8,9,10)) #Openness
cols <- c(cols_A, cols_E, cols_O)
std_AEO = std_quest[cols]
std_AEO #30columns## A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 O1 O2 O3 O4
## 1 4 3 4 2 4 2 3 5 2 3 2 3 4 2 5 5 1 2 3 1 4 3 4 4
## 2 3 4 2 4 4 4 3 3 2 3 4 4 5 5 5 4 1 1 1 1 1 2 3 2
## 3 5 5 5 5 5 5 5 2 1 2 3 3 5 2 5 1 1 3 2 2 5 4 4 3
## 4 4 5 4 4 4 5 4 3 1 2 3 2 4 4 4 2 2 3 1 4 4 3 4 4
## 5 3 3 2 4 3 4 4 3 4 4 2 2 3 1 4 3 5 5 4 3 5 2 5 4
## 6 4 4 4 3 4 3 4 3 3 3 3 3 4 2 4 3 2 3 2 3 4 3 4 4
## 7 4 4 4 4 4 4 5 3 2 3 3 4 3 4 3 4 2 3 3 2 4 4 3 4
## 8 5 5 4 3 5 5 4 4 2 2 2 5 5 5 5 3 2 1 2 2 3 4 4 4
## 9 5 3 3 4 4 1 2 3 2 2 2 2 5 3 3 3 2 2 3 1 2 2 4 2
## 10 4 4 5 4 5 4 5 1 1 2 5 4 4 4 5 4 1 2 1 1 0 5 4 4
## 11 1 5 2 3 5 3 4 4 3 5 5 5 5 4 5 3 1 1 2 1 5 5 5 5
## 12 5 4 5 5 5 5 5 1 0 1 4 3 4 3 4 4 2 2 2 3 5 2 4 4
## 13 3 3 2 5 3 4 2 3 1 1 1 1 5 1 4 1 1 5 1 3 4 2 2 4
## 14 2 3 3 4 2 2 4 2 3 2 2 2 2 3 2 3 3 3 3 1 2 2 1 3
## 15 4 5 2 4 4 4 4 2 2 2 2 4 5 4 4 3 1 3 1 2 2 3 4 4
## 16 5 4 3 3 4 4 4 3 3 3 1 4 5 3 4 4 1 3 2 1 3 2 3 3
## 17 3 3 4 2 3 4 4 4 2 2 2 2 4 2 4 1 1 3 2 2 2 2 2 2
## 18 5 5 5 5 5 5 5 4 1 1 5 5 5 2 5 1 1 2 4 1 5 3 4 5
## 19 4 3 3 3 3 2 3 5 3 4 2 5 5 4 4 4 1 2 3 3 2 4 3 4
## 20 3 5 4 4 4 4 5 4 1 2 2 4 4 4 4 2 2 4 1 1 4 4 4 5
## 21 4 4 4 4 4 4 5 3 2 4 2 2 4 2 4 3 3 4 2 4 5 2 4 4
## 22 4 4 4 4 3 3 5 2 2 2 2 4 4 4 4 2 2 2 2 2 4 2 4 2
## 23 4 5 4 4 4 3 4 5 2 4 2 4 5 2 5 5 1 3 1 5 2 2 3 3
## 24 4 4 4 1 4 5 4 5 2 3 2 3 5 2 4 3 5 5 2 3 5 4 5 5
## 25 5 4 4 4 5 5 4 2 2 1 4 2 4 2 4 1 3 4 2 4 4 4 3 5
## 26 3 4 3 4 3 3 4 2 2 4 2 4 3 3 3 2 4 4 3 3 4 3 3 4
## 27 2 4 2 4 4 5 2 2 1 2 2 4 2 4 2 2 2 2 1 1 2 4 4 4
## 28 4 5 4 5 4 4 4 2 1 2 3 3 3 2 4 2 2 2 2 4 2 4 4 3
## 29 4 4 5 3 4 2 4 4 2 2 1 2 4 2 4 2 2 5 1 2 4 2 4 4
## 30 4 3 4 4 3 3 4 2 2 3 1 3 3 2 3 2 2 4 3 1 4 2 3 3
## 31 4 4 4 4 4 4 3 4 2 3 1 2 3 2 4 1 3 2 2 5 4 2 4 4
## 32 4 3 4 3 4 4 4 4 2 2 2 3 5 2 4 2 2 3 4 2 3 2 4 2
## 33 2 4 5 2 5 5 4 1 2 1 3 5 4 2 5 1 1 4 3 4 5 5 4 4
## 34 4 5 5 4 4 5 4 2 2 1 4 4 4 4 5 4 2 2 2 4 2 1 2 1
## 35 3 3 1 2 4 4 4 2 4 4 1 1 2 1 4 4 4 5 4 1 5 1 5 3
## 36 3 3 3 5 4 4 5 3 1 3 4 4 5 5 5 0 1 2 1 1 3 1 3 3
## 37 1 3 1 4 4 4 3 4 2 3 3 3 5 3 5 1 1 3 2 1 4 4 4 3
## 38 3 4 5 5 4 4 5 2 2 4 5 5 5 2 5 5 1 4 3 2 4 1 4 3
## 39 1 5 1 4 5 5 2 2 1 5 5 5 5 4 5 5 1 1 1 1 1 1 1 1
## 40 4 2 3 3 2 3 3 3 3 4 1 2 4 1 4 3 1 5 1 3 4 3 4 4
## 41 5 5 5 5 5 5 5 1 1 1 3 3 4 2 5 4 2 2 2 2 4 2 4 4
## 42 4 4 3 3 3 3 4 4 3 3 2 3 3 2 3 5 3 4 2 4 4 3 2 4
## 43 4 4 5 2 5 4 5 2 2 2 4 4 2 4 4 4 4 1 2 2 2 2 3 3
## 44 4 4 4 4 3 3 4 3 1 2 2 3 4 3 4 3 2 2 2 2 4 2 4 4
## 45 4 5 4 4 4 4 5 4 1 2 3 3 1 2 3 2 2 4 2 1 1 4 4 5
## 46 4 4 4 4 5 5 4 3 1 1 4 4 3 2 4 2 1 1 2 2 4 4 5 4
## 47 4 4 3 3 4 3 4 3 3 3 3 3 5 3 4 1 1 3 2 3 3 4 4 4
## 48 5 5 5 5 5 5 4 5 2 1 4 5 5 5 5 5 5 1 1 1 5 5 5 5
## 49 3 1 2 4 2 2 2 4 1 3 3 2 3 2 4 1 2 2 3 2 2 1 2 1
## 50 4 5 4 4 5 5 5 4 1 3 4 4 4 4 4 1 1 2 2 2 4 5 4 4
## 51 4 4 4 4 5 4 4 3 2 2 3 2 4 1 4 2 1 3 2 4 4 2 4 2
## 52 4 4 4 2 4 4 4 3 2 2 3 3 2 3 3 2 3 4 2 4 0 4 4 4
## 53 3 4 3 4 5 2 5 5 2 1 4 5 5 3 5 4 1 2 1 2 2 3 3 2
## 54 5 4 4 4 4 4 4 4 3 4 4 5 5 4 5 5 2 3 1 5 4 2 2 5
## 55 5 4 5 4 4 4 4 4 1 4 3 4 5 4 5 1 1 2 1 1 4 5 4 3
## 56 5 5 5 5 4 4 5 3 1 1 2 3 4 2 4 2 2 4 5 3 5 1 4 3
## 57 3 4 3 3 2 4 4 4 4 2 2 3 2 2 3 2 3 3 2 2 4 4 4 4
## 58 4 4 4 4 4 4 4 2 2 4 2 2 4 2 5 2 1 5 1 2 5 2 4 4
## 59 5 5 5 5 4 5 5 2 1 3 4 3 5 5 4 4 1 2 1 2 3 2 3 3
## 60 1 4 3 4 5 3 2 3 0 2 4 5 5 3 4 4 3 4 4 1 4 5 1 4
## 61 2 3 2 3 4 3 4 4 2 3 2 3 5 3 4 2 1 2 2 2 2 2 4 2
## 62 4 3 4 5 3 3 4 3 1 1 3 1 5 1 4 3 1 5 1 1 3 1 3 3
## 63 3 3 5 3 3 3 5 2 2 3 1 4 3 2 4 3 3 5 2 1 4 1 4 4
## 64 5 5 4 5 5 3 4 1 1 3 3 3 4 4 4 4 1 2 2 1 4 2 3 4
## 65 4 3 4 4 5 4 4 4 3 2 2 3 4 3 4 1 2 2 2 2 4 2 2 2
## 66 2 3 3 4 4 3 4 1 1 2 1 1 3 1 5 2 2 2 2 3 4 2 5 2
## 67 3 3 1 4 4 3 3 3 3 4 4 4 3 4 4 4 4 3 3 3 4 4 4 4
## 68 1 3 1 1 3 4 2 5 5 3 3 3 4 2 4 3 2 4 1 1 3 1 2 2
## 69 4 5 4 0 4 4 4 4 3 2 3 4 4 2 4 3 2 3 2 2 3 2 3 3
## 70 2 2 4 4 2 1 4 4 4 2 1 1 2 1 4 5 2 5 1 1 4 1 1 5
## 71 5 5 5 3 5 4 5 4 1 3 4 4 5 4 5 5 4 2 1 3 4 3 1 5
## 72 5 5 5 5 4 4 5 2 2 1 1 1 4 2 5 2 1 4 2 1 2 1 3 1
## 73 4 5 5 4 4 4 5 3 1 2 3 4 5 3 5 4 3 3 3 1 5 3 4 3
## 74 4 5 5 4 4 4 4 3 2 3 5 2 4 4 4 5 4 4 2 2 4 4 3 4
## 75 4 4 4 5 5 4 4 4 2 2 1 3 5 4 4 4 1 2 1 1 4 1 4 1
## 76 2 3 2 3 4 3 4 2 3 5 3 3 5 3 4 4 2 4 2 1 4 1 2 3
## 77 5 3 5 5 5 5 5 3 1 3 5 5 5 5 5 3 1 3 1 3 3 1 5 3
## 78 5 2 3 4 4 3 4 2 1 1 1 2 5 1 3 3 1 4 4 2 2 2 3 3
## 79 2 4 4 2 4 3 4 5 1 3 4 3 4 2 3 4 4 4 3 2 2 4 4 5
## 80 4 4 5 4 4 4 4 3 2 2 2 3 4 2 4 2 2 4 0 3 2 4 4 3
## 81 2 4 4 3 4 4 4 3 2 3 2 2 5 2 4 3 2 3 2 3 4 3 3 3
## 82 4 4 4 3 5 3 4 3 3 3 5 5 5 4 5 5 4 1 1 1 5 2 4 3
## 83 4 4 3 4 4 4 4 4 0 2 1 1 4 1 3 2 3 5 2 0 3 3 4 2
## 84 3 3 3 4 4 3 4 3 2 2 2 2 4 2 4 1 2 4 2 5 3 2 4 3
## 85 5 5 5 5 4 5 5 2 1 2 3 4 3 1 4 2 3 4 1 3 2 2 3 3
## 86 3 4 3 4 3 4 0 3 3 2 1 2 2 1 4 1 4 4 3 5 3 3 4 4
## 87 4 4 3 3 4 3 3 3 3 3 1 1 2 2 3 1 2 4 3 1 4 3 4 5
## 88 4 5 5 4 5 5 4 2 1 4 5 5 5 4 4 5 4 1 2 1 2 5 2 2
## 89 2 2 3 3 3 3 4 2 2 2 2 2 2 1 2 2 3 4 2 4 3 4 2 3
## 90 4 4 3 4 4 4 4 2 1 2 2 3 5 3 4 2 1 2 2 1 4 2 5 3
## 91 2 4 4 4 4 4 4 4 2 2 2 4 4 3 4 2 1 2 1 2 4 2 3 4
## 92 4 5 4 4 4 4 4 3 2 4 4 5 4 4 4 4 4 2 2 1 4 3 4 2
## 93 2 3 3 3 3 2 3 5 4 4 1 1 3 1 3 1 4 4 1 2 3 3 3 3
## 94 5 4 5 5 5 4 5 1 1 1 3 2 3 2 4 2 2 4 3 3 4 2 4 2
## 95 5 4 5 5 4 4 4 2 1 4 1 1 4 4 4 2 2 2 2 1 2 4 4 2
## 96 4 1 4 3 1 1 3 5 2 1 1 1 1 1 1 1 5 5 5 1 5 1 5 4
## 97 4 3 5 5 4 3 4 5 1 3 2 4 4 4 4 2 4 4 1 1 3 5 4 2
## 98 5 5 5 5 5 4 5 2 1 2 4 4 5 5 5 5 1 1 1 2 5 2 4 2
## 99 2 4 3 3 2 3 4 4 3 3 1 2 5 3 3 2 1 5 1 2 2 3 3 2
## 100 2 3 3 4 3 3 3 3 2 2 2 2 3 3 4 2 3 4 2 2 4 3 4 5
## 101 2 4 4 4 4 4 4 3 2 2 3 3 4 4 4 3 2 3 3 3 4 2 4 4
## 102 2 5 4 2 3 3 4 4 4 5 3 3 4 2 4 4 2 4 3 3 1 3 4 4
## 103 4 3 5 4 4 4 5 2 2 2 3 2 4 3 4 4 2 5 2 2 4 2 2 3
## 104 2 5 4 2 5 3 4 3 3 2 2 4 2 5 3 2 2 2 1 2 4 2 4 5
## 105 5 5 5 4 4 4 4 2 2 2 4 4 4 4 4 2 2 2 2 2 4 4 4 4
## 106 5 5 4 5 5 4 4 4 1 4 3 3 5 3 4 3 1 4 1 2 4 3 3 4
## 107 2 4 2 3 3 3 4 3 2 1 1 4 4 4 0 4 2 3 2 4 3 2 4 2
## 108 4 4 4 4 4 4 4 0 1 2 2 5 4 3 5 5 1 3 4 1 0 4 5 4
## 109 4 4 4 4 3 4 4 2 2 2 3 2 4 1 4 1 2 5 1 4 4 2 4 3
## 110 3 4 4 4 4 4 4 2 2 2 3 3 1 1 3 1 4 2 2 2 3 4 3 3
## 111 5 4 4 5 4 5 5 2 1 1 1 2 3 4 3 2 1 2 1 4 4 3 4 3
## 112 4 3 3 3 3 2 4 3 2 3 3 4 3 3 4 5 2 2 3 1 4 3 4 3
## 113 2 4 2 3 3 3 3 5 2 3 1 1 3 1 4 2 2 4 2 1 3 1 4 2
## 114 2 2 1 1 2 1 2 4 4 5 1 1 2 1 1 1 4 5 4 1 5 2 4 4
## 115 4 4 5 5 4 4 4 5 1 1 1 1 4 4 4 1 1 2 2 2 5 1 5 5
## 116 5 5 5 4 4 4 5 2 1 2 4 5 5 4 5 5 1 2 1 4 4 4 2 4
## 117 1 1 1 2 2 3 4 4 4 4 2 1 4 1 4 1 2 5 2 4 2 2 4 4
## 118 4 5 4 4 5 4 4 4 3 3 4 4 5 4 3 2 1 2 1 1 4 3 4 4
## 119 3 4 4 5 3 3 4 2 3 2 1 4 5 3 4 4 3 3 2 2 5 2 5 3
## 120 3 4 4 5 5 1 4 1 4 4 1 1 4 1 2 1 5 5 4 3 5 1 3 4
## 121 2 5 4 5 2 5 5 1 3 2 1 4 4 2 2 3 2 5 4 4 5 2 4 4
## 122 4 5 5 4 4 5 4 2 1 4 2 4 5 5 4 5 1 1 1 1 4 2 3 4
## 123 2 3 2 5 3 3 4 5 2 2 3 4 2 4 2 3 4 1 4 2 4 2 4 2
## 124 5 5 5 4 5 5 4 5 1 2 5 0 5 2 5 3 1 5 1 1 4 4 4 3
## 125 5 4 5 4 3 4 4 3 1 3 1 4 3 2 3 2 3 3 2 3 4 3 2 4
## 126 4 4 2 4 4 4 4 3 2 3 2 2 4 3 4 2 2 3 2 3 2 2 4 2
## 127 4 4 4 4 4 4 4 4 2 2 2 2 4 2 4 2 2 2 2 2 2 2 4 4
## 128 4 4 4 4 4 4 3 2 2 4 2 2 4 3 4 3 3 3 2 4 4 3 3 4
## 129 3 4 4 4 3 3 3 3 3 2 2 2 4 2 3 3 1 2 3 3 3 2 4 3
## 130 0 0 0 4 4 0 4 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0
## 131 5 5 5 5 5 5 3 2 1 1 3 3 5 2 5 2 2 3 1 2 3 3 3 2
## 132 4 4 5 4 5 4 4 4 2 2 3 4 5 4 5 4 1 4 2 1 4 3 4 3
## 133 3 5 4 2 4 4 4 4 2 2 2 3 4 2 4 4 2 4 2 2 2 2 4 4
## 134 4 1 3 2 5 2 4 3 1 1 4 1 5 1 3 1 1 1 1 1 4 4 3 5
## 135 2 3 3 4 4 2 3 3 3 3 2 2 4 3 3 3 2 2 3 2 4 4 4 5
## 136 1 3 4 4 2 2 4 4 2 2 3 4 4 2 4 3 2 3 2 2 4 2 3 3
## 137 0 0 0 0 3 0 4 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0
## 138 2 3 4 3 4 4 5 4 4 1 3 1 5 1 5 4 2 4 3 3 4 1 4 2
## 139 3 3 3 1 2 1 2 1 3 1 1 1 5 1 3 3 1 5 3 5 3 1 1 1
## 140 4 4 4 4 4 3 4 4 2 2 3 4 5 4 4 2 2 2 2 1 5 2 4 3
## 141 4 2 4 4 4 4 4 3 1 1 1 4 3 2 4 2 3 3 2 2 2 1 3 2
## 142 4 4 3 4 4 4 4 3 2 2 3 3 4 3 4 4 2 2 1 2 4 5 4 4
## 143 4 4 4 4 3 4 4 4 2 2 2 4 4 4 4 3 2 2 2 2 2 3 3 2
## 144 2 4 2 4 4 4 4 4 2 4 1 1 4 1 4 1 4 4 2 5 2 2 4 1
## 145 2 4 3 3 4 3 3 5 3 3 2 1 5 1 4 4 1 5 1 3 4 1 4 3
## 146 4 4 5 4 4 3 4 2 2 2 2 2 4 2 4 3 1 3 2 1 4 2 4 4
## 147 5 4 5 5 5 5 5 2 1 1 1 1 3 1 5 1 4 5 2 2 5 4 5 5
## 148 4 3 4 4 4 4 4 3 2 2 5 4 4 3 4 4 4 3 3 1 5 4 4 5
## 149 4 4 4 4 4 4 4 2 2 3 2 4 3 4 4 2 3 3 1 2 4 4 4 4
## 150 2 3 3 2 3 3 4 2 3 2 1 2 4 1 3 4 2 5 2 5 4 2 3 4
## 151 5 4 4 5 5 5 4 2 1 2 4 3 4 4 5 4 1 1 1 2 4 4 5 5
## 152 4 4 3 4 4 4 4 3 1 4 4 4 4 4 4 2 2 2 2 2 3 3 2 3
## 153 3 4 5 4 4 4 4 4 2 2 3 3 4 3 4 2 1 4 1 1 4 4 4 2
## 154 5 5 4 5 4 4 4 1 1 1 2 2 4 1 4 1 1 4 2 4 2 2 1 3
## 155 4 3 3 3 3 3 4 2 3 2 3 3 4 3 4 1 3 2 3 2 4 4 3 5
## 156 4 5 5 0 4 3 5 2 2 3 3 4 4 3 4 3 2 3 3 3 4 2 4 4
## 157 4 4 4 4 4 4 5 2 2 2 3 3 4 4 3 4 3 1 1 1 2 2 4 4
## 158 4 4 4 1 4 4 4 5 3 2 2 1 4 2 4 4 2 5 4 1 4 4 4 5
## 159 4 4 4 4 4 4 4 2 2 2 4 4 4 2 4 4 2 2 2 4 4 4 4 3
## 160 5 5 5 3 5 5 5 3 3 4 3 2 1 3 2 4 4 3 5 4 4 4 3 5
## 161 1 4 1 4 4 4 1 4 4 4 4 4 4 4 4 2 2 2 1 1 5 2 4 5
## 162 4 4 4 4 4 4 4 4 1 2 2 2 4 3 4 1 1 4 2 2 3 3 4 3
## 163 5 5 5 5 5 5 4 2 1 1 4 5 5 5 5 5 1 1 1 1 2 5 5 4
## 164 5 4 5 4 4 4 4 2 1 1 2 2 2 2 4 3 4 4 2 4 4 4 4 4
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## 206 1 2 2 5 5 5
## 207 4 1 2 4 3 4
## 208 4 3 2 1 5 4
## 209 4 1 1 1 1 4
## 210 3 4 4 4 5 4
## 211 4 3 3 2 3 3
## 212 3 3 4 4 3 4
## 213 4 2 4 1 5 4
## 214 4 2 1 1 1 2
## 215 4 2 3 2 2 4
## 216 2 4 2 2 3 4
## 217 2 2 4 2 2 4
## 218 4 3 3 3 2 3
## 219 2 5 4 5 5 5
## 220 3 4 4 3 3 4
## 221 3 1 2 3 4 4
## 222 2 5 5 5 5 5
## 223 2 4 4 4 5 4
## 224 3 4 4 5 4 5
## 225 3 4 4 5 4 4
## 226 2 5 5 5 5 5
## 227 5 2 2 3 2 2
## 228 4 2 2 3 3 4
## 229 3 3 4 5 3 4
## 230 5 1 5 1 3 4
## 231 3 1 2 2 2 3
## 232 4 5 4 4 3 4
## 233 3 1 2 2 4 5
## 234 3 2 4 4 5 4
## 235 4 3 2 1 2 3
## 236 3 4 4 4 5 4
## 237 4 4 2 2 2 2
## 238 2 2 2 4 2 3
## 239 4 3 3 4 4 4
## 240 4 2 3 2 2 2
## 241 4 3 3 3 4 4
## 242 4 4 4 3 4 4
## 243 4 1 1 1 1 2
## 244 4 2 2 2 4 4
## 245 3 3 3 5 4 3
## 246 5 2 2 2 1 4
## 247 3 3 3 5 5 5
## 248 4 3 2 3 4 2
## 249 3 4 5 4 2 4
## 250 3 2 4 4 4 4
## 251 3 4 2 4 2 4
## 252 4 2 1 2 2 4
## 253 4 2 3 2 2 2
## 254 3 5 2 2 3 2
## 255 4 2 2 2 1 4
## 256 5 2 1 2 4 4
## 257 4 2 4 2 3 4
## 258 3 4 4 4 2 4
## 259 3 2 2 3 3 4
## 260 2 4 3 4 5 5
## 261 2 5 5 5 5 5
## 262 2 2 3 5 5 5
## 263 5 3 2 4 4 4
## 264 4 1 2 5 4 2
## 265 2 4 4 5 5 0
## 266 4 2 1 1 2 4
## 267 4 5 4 5 5 5
## 268 3 1 2 1 1 3
## 269 5 5 5 5 4 5
## 270 3 3 4 4 3 4
## 271 4 4 4 3 3 4
## 272 3 4 3 2 3 5
## 273 4 4 5 5 4 2
## 274 4 4 4 4 3 4
## 275 2 5 5 4 4 5
## 276 3 2 2 2 3 1
## 277 5 5 2 1 1 2
## 278 3 4 2 4 4 4
## 279 3 0 3 4 5 4
## 280 4 2 2 1 2 0
## 281 2 4 3 4 4 4
## 282 4 3 4 3 4 4
## 283 3 3 2 4 4 4
## 284 5 3 2 3 2 3
## 285 3 2 2 2 2 1
## 286 4 1 4 4 5 5
## 287 2 2 4 2 2 4
## 288 4 2 2 4 2 4
## 289 3 3 2 3 3 4
## 290 3 4 4 3 4 2
## 291 4 1 1 1 2 4
## 292 4 3 2 2 5 4
## 293 4 1 1 1 4 5
## 294 4 2 1 1 2 3
## 295 5 5 5 4 3 3
## 296 5 4 4 4 4 4
## 297 4 4 3 4 1 2
## 298 4 4 4 4 4 4
## 299 4 4 2 2 2 4
## 300 5 1 1 1 4 4
## 301 3 3 3 2 2 2
## 302 4 4 4 5 4 4
## 303 4 4 5 4 4 4
## 304 2 4 4 4 4 4
## 305 4 1 1 1 2 2
## 306 5 4 4 2 2 2
## 307 2 5 3 5 4 5
## 308 4 2 2 4 4 3
## 309 4 4 2 4 4 1
## 310 4 2 1 4 4 3
## 311 2 4 4 4 4 2
## 312 5 2 1 5 5 1
## 313 5 3 4 4 2 2
## 314 4 4 2 5 2 4
## 315 3 4 3 2 2 4
## 316 3 3 4 4 4 4
## 317 4 2 2 2 1 4
## 318 4 2 2 2 2 4
## 319 4 4 5 5 5 5
## 320 3 2 4 4 5 4
## 321 4 3 2 4 4 4
## 322 3 3 1 4 4 4
## 323 5 1 1 1 1 1
## 324 4 4 4 2 2 4
## 325 4 3 3 2 2 5
## 326 3 5 4 1 4 2
## 327 5 2 2 2 3 3
## 328 5 1 1 1 1 1
## 329 3 1 2 2 4 2
## 330 4 3 3 0 3 3
## 331 3 3 4 3 2 4
## 332 4 2 3 3 4 4
## 333 5 1 2 2 1 4
## 334 4 2 4 3 4 4
## 335 5 5 5 5 4 5
## 336 5 2 2 4 4 4
## 337 4 1 5 2 4 4
## 338 3 4 2 4 4 4
## 339 4 4 4 4 4 2
## 340 5 5 1 1 2 1
## 341 4 4 2 2 2 2
## 342 4 3 2 2 2 2
## 343 5 3 3 4 5 4
## 344 3 4 2 2 2 5
## 345 4 1 2 1 1 1
## 346 4 2 2 2 2 4
## 347 4 2 1 2 1 4
## 348 4 2 2 4 4 4
## 349 2 1 1 2 2 2
## 350 5 2 2 2 4 4
## 351 3 4 4 5 4 5
## 352 3 2 4 4 4 4
## 353 3 1 3 3 3 3
## 354 4 2 2 1 2 4
## 355 3 4 4 4 2 3
## 356 5 1 4 1 1 2
## 357 4 4 4 5 4 3
## 358 3 4 4 4 4 4
## 359 0 0 0 0 0 0
## 360 2 3 3 3 3 3
## 361 3 4 5 4 1 4
## 362 4 1 2 2 2 4
## 363 4 5 4 4 4 5
## 364 4 1 1 1 1 2
## 365 3 2 4 5 3 5
## 366 2 2 2 2 4 5
## 367 5 2 4 5 5 4
## 368 3 3 4 3 4 4
## 369 4 3 2 4 4 5
## 370 4 4 3 4 4 3
## 371 3 4 2 4 4 4
## 372 3 4 4 5 5 5
## 373 5 4 2 5 2 5
## 374 4 3 1 1 1 2
## 375 3 3 3 3 4 5
## 376 3 4 4 4 4 4
## 377 3 4 3 4 3 3
## 378 4 1 2 4 4 2
## 379 3 1 1 4 5 4
## 380 3 5 1 1 1 1
## 381 4 4 3 3 2 3
## 382 4 4 5 5 4 5Step 1 explore correlation and significance by visualisation
# 1 correlation matrix
perstdMatrix_AEO<-cor(std_AEO)
round(perstdMatrix_AEO, 2)## A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 E1 E2
## A1 1.00 0.39 0.56 0.43 0.42 0.45 0.31 -0.18 -0.30 -0.16 0.22 0.12
## A2 0.39 1.00 0.43 0.40 0.44 0.51 0.37 -0.17 -0.27 -0.08 0.36 0.37
## A3 0.56 0.43 1.00 0.33 0.30 0.44 0.41 -0.11 -0.28 -0.16 0.16 0.04
## A4 0.43 0.40 0.33 1.00 0.28 0.34 0.25 -0.24 -0.39 -0.18 0.18 0.15
## A5 0.42 0.44 0.30 0.28 1.00 0.46 0.26 -0.21 -0.37 -0.15 0.38 0.21
## A6 0.45 0.51 0.44 0.34 0.46 1.00 0.27 -0.09 -0.27 -0.07 0.29 0.20
## A7 0.31 0.37 0.41 0.25 0.26 0.27 1.00 -0.28 -0.28 -0.26 0.20 0.15
## A8 -0.18 -0.17 -0.11 -0.24 -0.21 -0.09 -0.28 1.00 0.30 0.24 -0.06 0.02
## A9 -0.30 -0.27 -0.28 -0.39 -0.37 -0.27 -0.28 0.30 1.00 0.30 -0.16 -0.10
## A10 -0.16 -0.08 -0.16 -0.18 -0.15 -0.07 -0.26 0.24 0.30 1.00 -0.03 0.09
## E1 0.22 0.36 0.16 0.18 0.38 0.29 0.20 -0.06 -0.16 -0.03 1.00 0.57
## E2 0.12 0.37 0.04 0.15 0.21 0.20 0.15 0.02 -0.10 0.09 0.57 1.00
## E3 0.28 0.36 0.21 0.26 0.29 0.23 0.15 0.03 -0.14 0.08 0.32 0.31
## E4 0.13 0.35 0.09 0.18 0.24 0.22 0.19 -0.03 -0.12 0.12 0.52 0.65
## E5 0.39 0.43 0.28 0.34 0.41 0.43 0.19 -0.06 -0.15 -0.05 0.40 0.28
## E6 0.15 0.29 0.17 0.10 0.18 0.08 0.12 -0.04 0.01 0.07 0.41 0.38
## E7 -0.08 -0.13 -0.10 -0.09 -0.21 -0.08 -0.17 0.14 0.24 0.17 -0.10 -0.02
## E8 -0.03 -0.13 0.05 -0.09 -0.25 -0.05 -0.11 0.08 0.22 0.07 -0.39 -0.53
## E9 -0.11 -0.08 -0.07 -0.15 -0.15 -0.14 -0.09 0.13 0.15 0.15 -0.07 0.04
## E10 0.02 0.01 0.05 -0.07 -0.10 0.10 -0.06 0.04 0.10 -0.01 -0.10 -0.20
## O1 0.08 0.09 0.11 0.08 -0.01 0.08 0.06 0.14 0.09 0.10 0.04 0.07
## O2 0.18 0.20 0.13 0.04 0.15 0.26 0.04 0.13 -0.04 -0.04 0.34 0.26
## O3 0.20 0.21 0.14 0.18 0.11 0.24 0.16 0.11 0.00 -0.03 0.08 0.11
## O4 0.12 0.14 0.13 -0.01 0.09 0.14 0.02 0.10 0.11 0.07 0.11 0.11
## O5 0.16 0.20 0.17 0.09 0.17 0.27 0.08 0.14 -0.02 0.07 0.14 0.09
## O6 -0.01 0.04 0.03 0.06 -0.08 -0.02 -0.04 0.05 0.17 0.05 -0.10 -0.06
## O7 0.04 0.08 0.07 0.08 0.01 0.05 -0.03 0.10 0.08 0.10 -0.04 -0.01
## O8 -0.11 0.04 -0.01 0.01 -0.07 -0.06 -0.03 0.09 0.13 0.15 -0.11 -0.07
## O9 0.00 0.06 0.09 0.03 -0.04 0.01 -0.08 0.00 0.08 0.12 -0.06 -0.02
## O10 -0.01 -0.03 0.01 0.04 -0.09 0.01 0.00 0.08 0.17 0.20 -0.13 -0.09
## E3 E4 E5 E6 E7 E8 E9 E10 O1 O2 O3 O4
## A1 0.28 0.13 0.39 0.15 -0.08 -0.03 -0.11 0.02 0.08 0.18 0.20 0.12
## A2 0.36 0.35 0.43 0.29 -0.13 -0.13 -0.08 0.01 0.09 0.20 0.21 0.14
## A3 0.21 0.09 0.28 0.17 -0.10 0.05 -0.07 0.05 0.11 0.13 0.14 0.13
## A4 0.26 0.18 0.34 0.10 -0.09 -0.09 -0.15 -0.07 0.08 0.04 0.18 -0.01
## A5 0.29 0.24 0.41 0.18 -0.21 -0.25 -0.15 -0.10 -0.01 0.15 0.11 0.09
## A6 0.23 0.22 0.43 0.08 -0.08 -0.05 -0.14 0.10 0.08 0.26 0.24 0.14
## A7 0.15 0.19 0.19 0.12 -0.17 -0.11 -0.09 -0.06 0.06 0.04 0.16 0.02
## A8 0.03 -0.03 -0.06 -0.04 0.14 0.08 0.13 0.04 0.14 0.13 0.11 0.10
## A9 -0.14 -0.12 -0.15 0.01 0.24 0.22 0.15 0.10 0.09 -0.04 0.00 0.11
## A10 0.08 0.12 -0.05 0.07 0.17 0.07 0.15 -0.01 0.10 -0.04 -0.03 0.07
## E1 0.32 0.52 0.40 0.41 -0.10 -0.39 -0.07 -0.10 0.04 0.34 0.08 0.11
## E2 0.31 0.65 0.28 0.38 -0.02 -0.53 0.04 -0.20 0.07 0.26 0.11 0.11
## E3 1.00 0.29 0.53 0.32 -0.43 -0.06 -0.12 0.00 0.08 0.00 0.14 -0.04
## E4 0.29 1.00 0.20 0.34 -0.11 -0.55 -0.09 -0.22 0.02 0.19 0.09 0.07
## E5 0.53 0.20 1.00 0.31 -0.26 -0.07 -0.20 -0.01 0.09 0.07 0.25 0.09
## E6 0.32 0.34 0.31 1.00 -0.04 -0.14 0.03 -0.15 0.04 -0.02 -0.03 0.08
## E7 -0.43 -0.11 -0.26 -0.04 1.00 0.15 0.24 0.06 0.17 0.17 0.03 0.17
## E8 -0.06 -0.55 -0.07 -0.14 0.15 1.00 0.15 0.26 0.14 -0.12 0.07 0.10
## E9 -0.12 -0.09 -0.20 0.03 0.24 0.15 1.00 0.08 0.19 0.06 0.08 0.11
## E10 0.00 -0.22 -0.01 -0.15 0.06 0.26 0.08 1.00 0.08 0.07 0.06 0.06
## O1 0.08 0.02 0.09 0.04 0.17 0.14 0.19 0.08 1.00 0.07 0.28 0.41
## O2 0.00 0.19 0.07 -0.02 0.17 -0.12 0.06 0.07 0.07 1.00 0.26 0.33
## O3 0.14 0.09 0.25 -0.03 0.03 0.07 0.08 0.06 0.28 0.26 1.00 0.34
## O4 -0.04 0.07 0.09 0.08 0.17 0.10 0.11 0.06 0.41 0.33 0.34 1.00
## O5 0.04 0.06 0.15 0.01 0.09 0.13 0.07 0.11 0.31 0.37 0.38 0.51
## O6 0.09 -0.01 0.10 0.10 0.08 0.08 0.01 -0.03 -0.04 -0.24 -0.21 -0.18
## O7 0.15 0.02 0.08 0.20 -0.02 0.08 0.01 0.01 -0.14 -0.22 -0.35 -0.22
## O8 0.14 -0.03 0.11 0.17 0.00 0.13 0.12 0.02 -0.03 -0.44 -0.24 -0.21
## O9 0.24 0.02 0.08 0.21 -0.07 0.08 0.07 0.07 -0.01 -0.37 -0.20 -0.22
## O10 0.16 -0.04 0.12 0.10 -0.03 0.19 0.07 0.04 0.10 -0.41 -0.06 -0.13
## O5 O6 O7 O8 O9 O10
## A1 0.16 -0.01 0.04 -0.11 0.00 -0.01
## A2 0.20 0.04 0.08 0.04 0.06 -0.03
## A3 0.17 0.03 0.07 -0.01 0.09 0.01
## A4 0.09 0.06 0.08 0.01 0.03 0.04
## A5 0.17 -0.08 0.01 -0.07 -0.04 -0.09
## A6 0.27 -0.02 0.05 -0.06 0.01 0.01
## A7 0.08 -0.04 -0.03 -0.03 -0.08 0.00
## A8 0.14 0.05 0.10 0.09 0.00 0.08
## A9 -0.02 0.17 0.08 0.13 0.08 0.17
## A10 0.07 0.05 0.10 0.15 0.12 0.20
## E1 0.14 -0.10 -0.04 -0.11 -0.06 -0.13
## E2 0.09 -0.06 -0.01 -0.07 -0.02 -0.09
## E3 0.04 0.09 0.15 0.14 0.24 0.16
## E4 0.06 -0.01 0.02 -0.03 0.02 -0.04
## E5 0.15 0.10 0.08 0.11 0.08 0.12
## E6 0.01 0.10 0.20 0.17 0.21 0.10
## E7 0.09 0.08 -0.02 0.00 -0.07 -0.03
## E8 0.13 0.08 0.08 0.13 0.08 0.19
## E9 0.07 0.01 0.01 0.12 0.07 0.07
## E10 0.11 -0.03 0.01 0.02 0.07 0.04
## O1 0.31 -0.04 -0.14 -0.03 -0.01 0.10
## O2 0.37 -0.24 -0.22 -0.44 -0.37 -0.41
## O3 0.38 -0.21 -0.35 -0.24 -0.20 -0.06
## O4 0.51 -0.18 -0.22 -0.21 -0.22 -0.13
## O5 1.00 -0.16 -0.14 -0.18 -0.16 -0.11
## O6 -0.16 1.00 0.50 0.47 0.33 0.26
## O7 -0.14 0.50 1.00 0.47 0.40 0.29
## O8 -0.18 0.47 0.47 1.00 0.60 0.47
## O9 -0.16 0.33 0.40 0.60 1.00 0.42
## O10 -0.11 0.26 0.29 0.47 0.42 1.00Hmisc::rcorr(as.matrix(std_AEO))## A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 E1 E2
## A1 1.00 0.39 0.56 0.43 0.42 0.45 0.31 -0.18 -0.30 -0.16 0.22 0.12
## A2 0.39 1.00 0.43 0.40 0.44 0.51 0.37 -0.17 -0.27 -0.08 0.36 0.37
## A3 0.56 0.43 1.00 0.33 0.30 0.44 0.41 -0.11 -0.28 -0.16 0.16 0.04
## A4 0.43 0.40 0.33 1.00 0.28 0.34 0.25 -0.24 -0.39 -0.18 0.18 0.15
## A5 0.42 0.44 0.30 0.28 1.00 0.46 0.26 -0.21 -0.37 -0.15 0.38 0.21
## A6 0.45 0.51 0.44 0.34 0.46 1.00 0.27 -0.09 -0.27 -0.07 0.29 0.20
## A7 0.31 0.37 0.41 0.25 0.26 0.27 1.00 -0.28 -0.28 -0.26 0.20 0.15
## A8 -0.18 -0.17 -0.11 -0.24 -0.21 -0.09 -0.28 1.00 0.30 0.24 -0.06 0.02
## A9 -0.30 -0.27 -0.28 -0.39 -0.37 -0.27 -0.28 0.30 1.00 0.30 -0.16 -0.10
## A10 -0.16 -0.08 -0.16 -0.18 -0.15 -0.07 -0.26 0.24 0.30 1.00 -0.03 0.09
## E1 0.22 0.36 0.16 0.18 0.38 0.29 0.20 -0.06 -0.16 -0.03 1.00 0.57
## E2 0.12 0.37 0.04 0.15 0.21 0.20 0.15 0.02 -0.10 0.09 0.57 1.00
## E3 0.28 0.36 0.21 0.26 0.29 0.23 0.15 0.03 -0.14 0.08 0.32 0.31
## E4 0.13 0.35 0.09 0.18 0.24 0.22 0.19 -0.03 -0.12 0.12 0.52 0.65
## E5 0.39 0.43 0.28 0.34 0.41 0.43 0.19 -0.06 -0.15 -0.05 0.40 0.28
## E6 0.15 0.29 0.17 0.10 0.18 0.08 0.12 -0.04 0.01 0.07 0.41 0.38
## E7 -0.08 -0.13 -0.10 -0.09 -0.21 -0.08 -0.17 0.14 0.24 0.17 -0.10 -0.02
## E8 -0.03 -0.13 0.05 -0.09 -0.25 -0.05 -0.11 0.08 0.22 0.07 -0.39 -0.53
## E9 -0.11 -0.08 -0.07 -0.15 -0.15 -0.14 -0.09 0.13 0.15 0.15 -0.07 0.04
## E10 0.02 0.01 0.05 -0.07 -0.10 0.10 -0.06 0.04 0.10 -0.01 -0.10 -0.20
## O1 0.08 0.09 0.11 0.08 -0.01 0.08 0.06 0.14 0.09 0.10 0.04 0.07
## O2 0.18 0.20 0.13 0.04 0.15 0.26 0.04 0.13 -0.04 -0.04 0.34 0.26
## O3 0.20 0.21 0.14 0.18 0.11 0.24 0.16 0.11 0.00 -0.03 0.08 0.11
## O4 0.12 0.14 0.13 -0.01 0.09 0.14 0.02 0.10 0.11 0.07 0.11 0.11
## O5 0.16 0.20 0.17 0.09 0.17 0.27 0.08 0.14 -0.02 0.07 0.14 0.09
## O6 -0.01 0.04 0.03 0.06 -0.08 -0.02 -0.04 0.05 0.17 0.05 -0.10 -0.06
## O7 0.04 0.08 0.07 0.08 0.01 0.05 -0.03 0.10 0.08 0.10 -0.04 -0.01
## O8 -0.11 0.04 -0.01 0.01 -0.07 -0.06 -0.03 0.09 0.13 0.15 -0.11 -0.07
## O9 0.00 0.06 0.09 0.03 -0.04 0.01 -0.08 0.00 0.08 0.12 -0.06 -0.02
## O10 -0.01 -0.03 0.01 0.04 -0.09 0.01 0.00 0.08 0.17 0.20 -0.13 -0.09
## E3 E4 E5 E6 E7 E8 E9 E10 O1 O2 O3 O4
## A1 0.28 0.13 0.39 0.15 -0.08 -0.03 -0.11 0.02 0.08 0.18 0.20 0.12
## A2 0.36 0.35 0.43 0.29 -0.13 -0.13 -0.08 0.01 0.09 0.20 0.21 0.14
## A3 0.21 0.09 0.28 0.17 -0.10 0.05 -0.07 0.05 0.11 0.13 0.14 0.13
## A4 0.26 0.18 0.34 0.10 -0.09 -0.09 -0.15 -0.07 0.08 0.04 0.18 -0.01
## A5 0.29 0.24 0.41 0.18 -0.21 -0.25 -0.15 -0.10 -0.01 0.15 0.11 0.09
## A6 0.23 0.22 0.43 0.08 -0.08 -0.05 -0.14 0.10 0.08 0.26 0.24 0.14
## A7 0.15 0.19 0.19 0.12 -0.17 -0.11 -0.09 -0.06 0.06 0.04 0.16 0.02
## A8 0.03 -0.03 -0.06 -0.04 0.14 0.08 0.13 0.04 0.14 0.13 0.11 0.10
## A9 -0.14 -0.12 -0.15 0.01 0.24 0.22 0.15 0.10 0.09 -0.04 0.00 0.11
## A10 0.08 0.12 -0.05 0.07 0.17 0.07 0.15 -0.01 0.10 -0.04 -0.03 0.07
## E1 0.32 0.52 0.40 0.41 -0.10 -0.39 -0.07 -0.10 0.04 0.34 0.08 0.11
## E2 0.31 0.65 0.28 0.38 -0.02 -0.53 0.04 -0.20 0.07 0.26 0.11 0.11
## E3 1.00 0.29 0.53 0.32 -0.43 -0.06 -0.12 0.00 0.08 0.00 0.14 -0.04
## E4 0.29 1.00 0.20 0.34 -0.11 -0.55 -0.09 -0.22 0.02 0.19 0.09 0.07
## E5 0.53 0.20 1.00 0.31 -0.26 -0.07 -0.20 -0.01 0.09 0.07 0.25 0.09
## E6 0.32 0.34 0.31 1.00 -0.04 -0.14 0.03 -0.15 0.04 -0.02 -0.03 0.08
## E7 -0.43 -0.11 -0.26 -0.04 1.00 0.15 0.24 0.06 0.17 0.17 0.03 0.17
## E8 -0.06 -0.55 -0.07 -0.14 0.15 1.00 0.15 0.26 0.14 -0.12 0.07 0.10
## E9 -0.12 -0.09 -0.20 0.03 0.24 0.15 1.00 0.08 0.19 0.06 0.08 0.11
## E10 0.00 -0.22 -0.01 -0.15 0.06 0.26 0.08 1.00 0.08 0.07 0.06 0.06
## O1 0.08 0.02 0.09 0.04 0.17 0.14 0.19 0.08 1.00 0.07 0.28 0.41
## O2 0.00 0.19 0.07 -0.02 0.17 -0.12 0.06 0.07 0.07 1.00 0.26 0.33
## O3 0.14 0.09 0.25 -0.03 0.03 0.07 0.08 0.06 0.28 0.26 1.00 0.34
## O4 -0.04 0.07 0.09 0.08 0.17 0.10 0.11 0.06 0.41 0.33 0.34 1.00
## O5 0.04 0.06 0.15 0.01 0.09 0.13 0.07 0.11 0.31 0.37 0.38 0.51
## O6 0.09 -0.01 0.10 0.10 0.08 0.08 0.01 -0.03 -0.04 -0.24 -0.21 -0.18
## O7 0.15 0.02 0.08 0.20 -0.02 0.08 0.01 0.01 -0.14 -0.22 -0.35 -0.22
## O8 0.14 -0.03 0.11 0.17 0.00 0.13 0.12 0.02 -0.03 -0.44 -0.24 -0.21
## O9 0.24 0.02 0.08 0.21 -0.07 0.08 0.07 0.07 -0.01 -0.37 -0.20 -0.22
## O10 0.16 -0.04 0.12 0.10 -0.03 0.19 0.07 0.04 0.10 -0.41 -0.06 -0.13
## O5 O6 O7 O8 O9 O10
## A1 0.16 -0.01 0.04 -0.11 0.00 -0.01
## A2 0.20 0.04 0.08 0.04 0.06 -0.03
## A3 0.17 0.03 0.07 -0.01 0.09 0.01
## A4 0.09 0.06 0.08 0.01 0.03 0.04
## A5 0.17 -0.08 0.01 -0.07 -0.04 -0.09
## A6 0.27 -0.02 0.05 -0.06 0.01 0.01
## A7 0.08 -0.04 -0.03 -0.03 -0.08 0.00
## A8 0.14 0.05 0.10 0.09 0.00 0.08
## A9 -0.02 0.17 0.08 0.13 0.08 0.17
## A10 0.07 0.05 0.10 0.15 0.12 0.20
## E1 0.14 -0.10 -0.04 -0.11 -0.06 -0.13
## E2 0.09 -0.06 -0.01 -0.07 -0.02 -0.09
## E3 0.04 0.09 0.15 0.14 0.24 0.16
## E4 0.06 -0.01 0.02 -0.03 0.02 -0.04
## E5 0.15 0.10 0.08 0.11 0.08 0.12
## E6 0.01 0.10 0.20 0.17 0.21 0.10
## E7 0.09 0.08 -0.02 0.00 -0.07 -0.03
## E8 0.13 0.08 0.08 0.13 0.08 0.19
## E9 0.07 0.01 0.01 0.12 0.07 0.07
## E10 0.11 -0.03 0.01 0.02 0.07 0.04
## O1 0.31 -0.04 -0.14 -0.03 -0.01 0.10
## O2 0.37 -0.24 -0.22 -0.44 -0.37 -0.41
## O3 0.38 -0.21 -0.35 -0.24 -0.20 -0.06
## O4 0.51 -0.18 -0.22 -0.21 -0.22 -0.13
## O5 1.00 -0.16 -0.14 -0.18 -0.16 -0.11
## O6 -0.16 1.00 0.50 0.47 0.33 0.26
## O7 -0.14 0.50 1.00 0.47 0.40 0.29
## O8 -0.18 0.47 0.47 1.00 0.60 0.47
## O9 -0.16 0.33 0.40 0.60 1.00 0.42
## O10 -0.11 0.26 0.29 0.47 0.42 1.00
##
## n= 382
##
##
## P
## A1 A2 A3 A4 A5 A6 A7 A8 A9 A10
## A1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0000 0.0023
## A2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0008 0.0000 0.1215
## A3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0263 0.0000 0.0014
## A4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005
## A5 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0030
## A6 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0667 0.0000 0.1764
## A7 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## A8 0.0004 0.0008 0.0263 0.0000 0.0000 0.0667 0.0000 0.0000 0.0000
## A9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## A10 0.0023 0.1215 0.0014 0.0005 0.0030 0.1764 0.0000 0.0000 0.0000
## E1 0.0000 0.0000 0.0023 0.0003 0.0000 0.0000 0.0001 0.2708 0.0018 0.5838
## E2 0.0231 0.0000 0.4290 0.0026 0.0000 0.0000 0.0035 0.6496 0.0459 0.0916
## E3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0024 0.5344 0.0047 0.1430
## E4 0.0136 0.0000 0.0959 0.0004 0.0000 0.0000 0.0002 0.5358 0.0172 0.0222
## E5 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.2217 0.0025 0.2862
## E6 0.0025 0.0000 0.0011 0.0542 0.0003 0.1088 0.0222 0.3954 0.8100 0.1567
## E7 0.1106 0.0102 0.0429 0.0813 0.0000 0.1330 0.0008 0.0057 0.0000 0.0006
## E8 0.5017 0.0127 0.3520 0.0798 0.0000 0.2889 0.0348 0.1319 0.0000 0.1577
## E9 0.0287 0.1235 0.1881 0.0035 0.0043 0.0057 0.0717 0.0139 0.0027 0.0028
## E10 0.6691 0.8495 0.3647 0.1949 0.0541 0.0491 0.2741 0.4655 0.0492 0.8995
## O1 0.1121 0.0792 0.0354 0.1030 0.8085 0.1021 0.2092 0.0049 0.0898 0.0495
## O2 0.0005 0.0000 0.0143 0.4641 0.0030 0.0000 0.4932 0.0141 0.4371 0.4804
## O3 0.0000 0.0000 0.0050 0.0004 0.0341 0.0000 0.0021 0.0335 0.9593 0.5889
## O4 0.0159 0.0064 0.0134 0.7820 0.0664 0.0049 0.6429 0.0464 0.0359 0.1692
## O5 0.0023 0.0000 0.0010 0.0758 0.0007 0.0000 0.1059 0.0063 0.6362 0.1816
## O6 0.8157 0.4647 0.5769 0.2564 0.1108 0.6307 0.4799 0.3270 0.0006 0.3676
## O7 0.4925 0.1228 0.1835 0.1203 0.8227 0.2837 0.5634 0.0453 0.1398 0.0403
## O8 0.0338 0.3911 0.8716 0.9152 0.1695 0.2483 0.5334 0.0909 0.0135 0.0039
## O9 0.9410 0.2090 0.0770 0.5057 0.3861 0.7737 0.1019 0.9566 0.1191 0.0166
## O10 0.9156 0.5071 0.8137 0.4404 0.0759 0.8476 0.9957 0.0988 0.0009 0.0001
## E1 E2 E3 E4 E5 E6 E7 E8 E9 E10
## A1 0.0000 0.0231 0.0000 0.0136 0.0000 0.0025 0.1106 0.5017 0.0287 0.6691
## A2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0102 0.0127 0.1235 0.8495
## A3 0.0023 0.4290 0.0000 0.0959 0.0000 0.0011 0.0429 0.3520 0.1881 0.3647
## A4 0.0003 0.0026 0.0000 0.0004 0.0000 0.0542 0.0813 0.0798 0.0035 0.1949
## A5 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0000 0.0000 0.0043 0.0541
## A6 0.0000 0.0000 0.0000 0.0000 0.0000 0.1088 0.1330 0.2889 0.0057 0.0491
## A7 0.0001 0.0035 0.0024 0.0002 0.0003 0.0222 0.0008 0.0348 0.0717 0.2741
## A8 0.2708 0.6496 0.5344 0.5358 0.2217 0.3954 0.0057 0.1319 0.0139 0.4655
## A9 0.0018 0.0459 0.0047 0.0172 0.0025 0.8100 0.0000 0.0000 0.0027 0.0492
## A10 0.5838 0.0916 0.1430 0.0222 0.2862 0.1567 0.0006 0.1577 0.0028 0.8995
## E1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0624 0.0000 0.1438 0.0606
## E2 0.0000 0.0000 0.0000 0.0000 0.0000 0.6479 0.0000 0.4709 0.0000
## E3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2091 0.0156 0.9592
## E4 0.0000 0.0000 0.0000 0.0001 0.0000 0.0274 0.0000 0.0653 0.0000
## E5 0.0000 0.0000 0.0000 0.0001 0.0000 0.0000 0.1619 0.0001 0.8689
## E6 0.0000 0.0000 0.0000 0.0000 0.0000 0.4142 0.0046 0.5459 0.0040
## E7 0.0624 0.6479 0.0000 0.0274 0.0000 0.4142 0.0028 0.0000 0.2656
## E8 0.0000 0.0000 0.2091 0.0000 0.1619 0.0046 0.0028 0.0029 0.0000
## E9 0.1438 0.4709 0.0156 0.0653 0.0001 0.5459 0.0000 0.0029 0.1054
## E10 0.0606 0.0000 0.9592 0.0000 0.8689 0.0040 0.2656 0.0000 0.1054
## O1 0.4575 0.1436 0.1264 0.6898 0.0813 0.4095 0.0008 0.0063 0.0001 0.1218
## O2 0.0000 0.0000 0.9252 0.0001 0.1813 0.6935 0.0010 0.0176 0.2352 0.1830
## O3 0.1023 0.0259 0.0049 0.0794 0.0000 0.5987 0.6129 0.1853 0.0983 0.2632
## O4 0.0271 0.0293 0.4556 0.2045 0.0770 0.1100 0.0010 0.0581 0.0396 0.2124
## O5 0.0047 0.0665 0.4175 0.2669 0.0027 0.8687 0.0707 0.0093 0.1657 0.0296
## O6 0.0521 0.2105 0.0919 0.8051 0.0434 0.0586 0.1222 0.1359 0.8497 0.5962
## O7 0.4783 0.7911 0.0042 0.7669 0.1138 0.0001 0.7446 0.1170 0.8768 0.8659
## O8 0.0293 0.1947 0.0062 0.5721 0.0294 0.0006 0.9588 0.0136 0.0179 0.6887
## O9 0.2474 0.7180 0.0000 0.7038 0.1173 0.0000 0.1452 0.1159 0.1562 0.1546
## O10 0.0110 0.0954 0.0018 0.4578 0.0213 0.0472 0.5176 0.0001 0.1568 0.4204
## O1 O2 O3 O4 O5 O6 O7 O8 O9 O10
## A1 0.1121 0.0005 0.0000 0.0159 0.0023 0.8157 0.4925 0.0338 0.9410 0.9156
## A2 0.0792 0.0000 0.0000 0.0064 0.0000 0.4647 0.1228 0.3911 0.2090 0.5071
## A3 0.0354 0.0143 0.0050 0.0134 0.0010 0.5769 0.1835 0.8716 0.0770 0.8137
## A4 0.1030 0.4641 0.0004 0.7820 0.0758 0.2564 0.1203 0.9152 0.5057 0.4404
## A5 0.8085 0.0030 0.0341 0.0664 0.0007 0.1108 0.8227 0.1695 0.3861 0.0759
## A6 0.1021 0.0000 0.0000 0.0049 0.0000 0.6307 0.2837 0.2483 0.7737 0.8476
## A7 0.2092 0.4932 0.0021 0.6429 0.1059 0.4799 0.5634 0.5334 0.1019 0.9957
## A8 0.0049 0.0141 0.0335 0.0464 0.0063 0.3270 0.0453 0.0909 0.9566 0.0988
## A9 0.0898 0.4371 0.9593 0.0359 0.6362 0.0006 0.1398 0.0135 0.1191 0.0009
## A10 0.0495 0.4804 0.5889 0.1692 0.1816 0.3676 0.0403 0.0039 0.0166 0.0001
## E1 0.4575 0.0000 0.1023 0.0271 0.0047 0.0521 0.4783 0.0293 0.2474 0.0110
## E2 0.1436 0.0000 0.0259 0.0293 0.0665 0.2105 0.7911 0.1947 0.7180 0.0954
## E3 0.1264 0.9252 0.0049 0.4556 0.4175 0.0919 0.0042 0.0062 0.0000 0.0018
## E4 0.6898 0.0001 0.0794 0.2045 0.2669 0.8051 0.7669 0.5721 0.7038 0.4578
## E5 0.0813 0.1813 0.0000 0.0770 0.0027 0.0434 0.1138 0.0294 0.1173 0.0213
## E6 0.4095 0.6935 0.5987 0.1100 0.8687 0.0586 0.0001 0.0006 0.0000 0.0472
## E7 0.0008 0.0010 0.6129 0.0010 0.0707 0.1222 0.7446 0.9588 0.1452 0.5176
## E8 0.0063 0.0176 0.1853 0.0581 0.0093 0.1359 0.1170 0.0136 0.1159 0.0001
## E9 0.0001 0.2352 0.0983 0.0396 0.1657 0.8497 0.8768 0.0179 0.1562 0.1568
## E10 0.1218 0.1830 0.2632 0.2124 0.0296 0.5962 0.8659 0.6887 0.1546 0.4204
## O1 0.1520 0.0000 0.0000 0.0000 0.4146 0.0047 0.5479 0.8552 0.0594
## O2 0.1520 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## O3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2722
## O4 0.0000 0.0000 0.0000 0.0000 0.0005 0.0000 0.0000 0.0000 0.0097
## O5 0.0000 0.0000 0.0000 0.0000 0.0022 0.0077 0.0004 0.0021 0.0347
## O6 0.4146 0.0000 0.0000 0.0005 0.0022 0.0000 0.0000 0.0000 0.0000
## O7 0.0047 0.0000 0.0000 0.0000 0.0077 0.0000 0.0000 0.0000 0.0000
## O8 0.5479 0.0000 0.0000 0.0000 0.0004 0.0000 0.0000 0.0000 0.0000
## O9 0.8552 0.0000 0.0000 0.0000 0.0021 0.0000 0.0000 0.0000 0.0000
## O10 0.0594 0.0000 0.2722 0.0097 0.0347 0.0000 0.0000 0.0000 0.0000pMat <- ggcorrplot::cor_pmat(std_AEO)
ggcorrplot::ggcorrplot(perstdMatrix_AEO, tl.cex = 8, title="Correlation Matric for Stduent Personality data (A,E,O)") + theme(axis.text.x = element_text(margin=ggplot2::margin(-2,0,0,0)),
axis.text.y = element_text(margin=ggplot2::margin(0,-2,0,0)),
panel.grid.minor = element_line(size=10))
#Showing X for non-significant correlations
ggcorrplot::ggcorrplot(perstdMatrix_AEO, tl.cex = 8, title = "Correlation matrix for Stduent Personality data (A,E,O)", p.mat = pMat, sig.level = 0.05)
#Showing lower diagonal
ggcorrplot::ggcorrplot(perstdMatrix_AEO, tl.cex = 8, title = "Correlation matrix for Stduent Personality data (A,E,O)", p.mat = pMat, sig.level = 0.05, type="lower")
#Overlay plot with a white grid to space things out for non-significant correlations
ggcorrplot(perstdMatrix_AEO, sig.level=0.05, lab_size = 4.5, p.mat = NULL,
insig = c("pch", "blank"), pch = 1, pch.col = "black", pch.cex =1,
tl.cex = 8) +
theme(axis.text.x = element_text(margin=ggplot2::margin(-2,0,0,0)),
axis.text.y = element_text(margin=ggplot2::margin(0,-2,0,0)),
panel.grid.minor = element_line(size=10)) +
geom_tile(fill="white") +
geom_tile(height=0.8, width=0.8)
#Showing the co-coefficients (this will be messy given the number of variables)
ggcorrplot::ggcorrplot(perstdMatrix_AEO, lab=TRUE, title = "Correlation matrix for Stduent Personality data (A,E,O)", type="lower")
#Visualization of correlations using shade
#corrplot parameters method = c("circle", "square", "ellipse", "number", "shade",
#"color", "pie")
#type = c("full", "lower", "upper"),
corrplot::corrplot(perstdMatrix_AEO, method="ellipse")
corrplot::corrplot(perstdMatrix_AEO, method="circle", type="upper")
corrplot::corrplot(perstdMatrix_AEO, method="number")
#About significance level at 0.05, and Non-significant
res_max_AEO <- corrplot::cor.mtest(perstdMatrix_AEO, conf.level = .95)
res_max_AEO## $p
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.000000e+00 5.504347e-07 4.391808e-10 1.341975e-07 1.631543e-07
## [2,] 5.504347e-07 0.000000e+00 2.782554e-06 5.688783e-07 4.798226e-09
## [3,] 4.391808e-10 2.782554e-06 0.000000e+00 1.117157e-05 3.015084e-05
## [4,] 1.341975e-07 5.688783e-07 1.117157e-05 0.000000e+00 1.122540e-05
## [5,] 1.631543e-07 4.798226e-09 3.015084e-05 1.122540e-05 0.000000e+00
## [6,] 2.710448e-08 1.068455e-08 6.381878e-07 7.136243e-06 1.208482e-08
## [7,] 9.868634e-06 2.165878e-06 1.268635e-06 5.300317e-05 3.294970e-05
## [8,] 9.383381e-05 6.708039e-05 3.249203e-04 2.252491e-05 1.696491e-04
## [9,] 3.032036e-08 1.492202e-08 3.535772e-07 3.991416e-09 6.300134e-09
## [10,] 6.733287e-05 8.084840e-04 5.167581e-05 2.196294e-04 7.373562e-04
## [11,] 4.925545e-03 1.586194e-05 4.528479e-02 8.329184e-03 7.781357e-06
## [12,] 1.030871e-01 5.359847e-04 3.667632e-01 5.629253e-02 2.375918e-03
## [13,] 4.822223e-03 1.847247e-04 1.886750e-02 1.625082e-03 4.814029e-04
## [14,] 6.701226e-02 2.400931e-04 2.216088e-01 2.608265e-02 1.022558e-03
## [15,] 1.440087e-05 7.172518e-07 6.589347e-04 2.040749e-05 5.105688e-07
## [16,] 2.123642e-01 1.137957e-02 2.855631e-01 1.513330e-01 2.901824e-02
## [17,] 3.980168e-03 3.582018e-04 4.753370e-03 2.486038e-03 3.184991e-04
## [18,] 5.583546e-02 7.209200e-04 2.274162e-01 2.574517e-02 4.103455e-04
## [19,] 1.074362e-03 7.147006e-04 4.643191e-03 7.373452e-04 5.582033e-04
## [20,] 3.548733e-01 9.277706e-02 5.559354e-01 1.289755e-01 6.480022e-02
## [21,] 7.718206e-01 5.248358e-01 8.213617e-01 6.139377e-01 4.225383e-01
## [22,] 8.538797e-02 7.695936e-02 2.611049e-01 4.825464e-01 5.604060e-02
## [23,] 5.358152e-02 1.084108e-01 1.549420e-01 1.736191e-01 1.314766e-01
## [24,] 5.605518e-01 7.261162e-01 7.124093e-01 6.764740e-01 6.325799e-01
## [25,] 1.868381e-01 2.660175e-01 2.631936e-01 6.126443e-01 1.895497e-01
## [26,] 1.035506e-01 1.470258e-01 2.469688e-01 4.909143e-01 7.152553e-02
## [27,] 2.653185e-01 3.916392e-01 5.016447e-01 7.505951e-01 3.029456e-01
## [28,] 3.060052e-02 9.984162e-02 1.431717e-01 2.903104e-01 4.939281e-02
## [29,] 1.717176e-01 3.093329e-01 4.606382e-01 6.061081e-01 1.763684e-01
## [30,] 6.628234e-02 4.416878e-02 1.690011e-01 3.173599e-01 3.012342e-02
## [,6] [,7] [,8] [,9] [,10]
## [1,] 2.710448e-08 9.868634e-06 9.383381e-05 3.032036e-08 6.733287e-05
## [2,] 1.068455e-08 2.165878e-06 6.708039e-05 1.492202e-08 8.084840e-04
## [3,] 6.381878e-07 1.268635e-06 3.249203e-04 3.535772e-07 5.167581e-05
## [4,] 7.136243e-06 5.300317e-05 2.252491e-05 3.991416e-09 2.196294e-04
## [5,] 1.208482e-08 3.294970e-05 1.696491e-04 6.300134e-09 7.373562e-04
## [6,] 0.000000e+00 6.495440e-05 1.050475e-03 8.133032e-08 7.167675e-04
## [7,] 6.495440e-05 0.000000e+00 1.293389e-05 7.748611e-07 2.080280e-05
## [8,] 1.050475e-03 1.293389e-05 0.000000e+00 6.101424e-05 1.464676e-03
## [9,] 8.133032e-08 7.748611e-07 6.101424e-05 0.000000e+00 1.086680e-04
## [10,] 7.167675e-04 2.080280e-05 1.464676e-03 1.086680e-04 0.000000e+00
## [11,] 8.781252e-04 5.157426e-03 3.082872e-02 4.738552e-04 6.520207e-02
## [12,] 3.009594e-02 4.490581e-02 1.897742e-01 1.225587e-02 4.621570e-01
## [13,] 7.069688e-03 1.832264e-02 4.538177e-02 1.354429e-03 1.676813e-01
## [14,] 1.805569e-02 1.868581e-02 9.107936e-02 6.001965e-03 4.571562e-01
## [15,] 5.535000e-06 1.438680e-03 3.708493e-03 3.691793e-05 7.734474e-03
## [16,] 3.450750e-01 1.451274e-01 7.404810e-02 1.032365e-01 5.929026e-01
## [17,] 4.333097e-03 2.053054e-03 2.149661e-02 1.253611e-03 4.317672e-02
## [18,] 2.067321e-02 1.981231e-02 1.260462e-01 5.748614e-03 2.970802e-01
## [19,] 4.290536e-04 6.280721e-03 3.150835e-02 4.966822e-03 3.838665e-02
## [20,] 5.073137e-01 1.624956e-01 4.867809e-01 2.016888e-01 9.696611e-01
## [21,] 7.561117e-01 7.563079e-01 3.185340e-01 5.785012e-01 7.819919e-01
## [22,] 1.926998e-02 2.883082e-01 9.505534e-01 1.252769e-01 1.757589e-01
## [23,] 2.761958e-02 1.164382e-01 7.988963e-01 1.549538e-01 1.219640e-01
## [24,] 3.896448e-01 8.929203e-01 5.655442e-01 9.801195e-01 7.372727e-01
## [25,] 4.795904e-02 4.345925e-01 8.246451e-01 2.721989e-01 3.634062e-01
## [26,] 4.737378e-02 1.564316e-01 7.608188e-01 1.265031e-01 4.100636e-01
## [27,] 1.874755e-01 2.709774e-01 9.016666e-01 4.494210e-01 4.081194e-01
## [28,] 1.875137e-02 1.134749e-01 6.414055e-01 1.196406e-01 1.430166e-01
## [29,] 1.060368e-01 2.022507e-01 8.932577e-01 3.573646e-01 2.676161e-01
## [30,] 3.326884e-02 1.385428e-01 5.420068e-01 7.701168e-02 8.580533e-02
## [,11] [,12] [,13] [,14] [,15]
## [1,] 4.925545e-03 1.030871e-01 4.822223e-03 6.701226e-02 1.440087e-05
## [2,] 1.586194e-05 5.359847e-04 1.847247e-04 2.400931e-04 7.172518e-07
## [3,] 4.528479e-02 3.667632e-01 1.886750e-02 2.216088e-01 6.589347e-04
## [4,] 8.329184e-03 5.629253e-02 1.625082e-03 2.608265e-02 2.040749e-05
## [5,] 7.781357e-06 2.375918e-03 4.814029e-04 1.022558e-03 5.105688e-07
## [6,] 8.781252e-04 3.009594e-02 7.069688e-03 1.805569e-02 5.535000e-06
## [7,] 5.157426e-03 4.490581e-02 1.832264e-02 1.868581e-02 1.438680e-03
## [8,] 3.082872e-02 1.897742e-01 4.538177e-02 9.107936e-02 3.708493e-03
## [9,] 4.738552e-04 1.225587e-02 1.354429e-03 6.001965e-03 3.691793e-05
## [10,] 6.520207e-02 4.621570e-01 1.676813e-01 4.571562e-01 7.734474e-03
## [11,] 0.000000e+00 1.797151e-10 1.262540e-03 1.858329e-09 9.930986e-05
## [12,] 1.797151e-10 0.000000e+00 5.863092e-03 6.120789e-14 6.191882e-03
## [13,] 1.262540e-03 5.863092e-03 0.000000e+00 2.576874e-03 3.767340e-08
## [14,] 1.858329e-09 6.120789e-14 2.576874e-03 0.000000e+00 5.372016e-03
## [15,] 9.930986e-05 6.191882e-03 3.767340e-08 5.372016e-03 0.000000e+00
## [16,] 2.323897e-04 2.451425e-04 1.183906e-03 2.170825e-04 4.972471e-03
## [17,] 1.072206e-02 6.410554e-02 3.112729e-10 1.754994e-02 1.719929e-06
## [18,] 4.346964e-09 1.498205e-12 9.946997e-03 9.373691e-14 8.065684e-03
## [19,] 1.058960e-02 1.081299e-01 9.207503e-04 2.260795e-02 3.775302e-05
## [20,] 9.793107e-03 9.713337e-04 9.711614e-02 5.161299e-04 1.072858e-01
## [21,] 5.205232e-01 6.577608e-01 2.467267e-01 3.833945e-01 4.538421e-01
## [22,] 3.255580e-03 1.691639e-02 7.251610e-01 6.376286e-02 4.973528e-01
## [23,] 2.152283e-01 3.309055e-01 7.480777e-01 5.196893e-01 1.494924e-01
## [24,] 4.554373e-01 5.723150e-01 1.635968e-01 9.252130e-01 8.181193e-01
## [25,] 2.939411e-01 5.758748e-01 5.192902e-01 8.510021e-01 5.910189e-01
## [26,] 2.607947e-02 7.530589e-02 9.977001e-01 1.891053e-01 5.161689e-01
## [27,] 1.258270e-01 2.101436e-01 4.948236e-01 4.244176e-01 7.852834e-01
## [28,] 1.514030e-02 6.190711e-02 7.417603e-01 1.516430e-01 4.720934e-01
## [29,] 7.175189e-02 1.657445e-01 2.706078e-01 3.544423e-01 8.115429e-01
## [30,] 4.360658e-03 2.107310e-02 7.632926e-01 6.689155e-02 4.985996e-01
## [,16] [,17] [,18] [,19] [,20]
## [1,] 0.2123642466 3.980168e-03 5.583546e-02 1.074362e-03 0.3548732641
## [2,] 0.0113795677 3.582018e-04 7.209200e-04 7.147006e-04 0.0927770631
## [3,] 0.2855630860 4.753370e-03 2.274162e-01 4.643191e-03 0.5559353581
## [4,] 0.1513329505 2.486038e-03 2.574517e-02 7.373452e-04 0.1289754893
## [5,] 0.0290182400 3.184991e-04 4.103455e-04 5.582033e-04 0.0648002181
## [6,] 0.3450750027 4.333097e-03 2.067321e-02 4.290536e-04 0.5073136817
## [7,] 0.1451274056 2.053054e-03 1.981231e-02 6.280721e-03 0.1624955812
## [8,] 0.0740481010 2.149661e-02 1.260462e-01 3.150835e-02 0.4867808504
## [9,] 0.1032364658 1.253611e-03 5.748614e-03 4.966822e-03 0.2016888222
## [10,] 0.5929025751 4.317672e-02 2.970802e-01 3.838665e-02 0.9696611081
## [11,] 0.0002323897 1.072206e-02 4.346964e-09 1.058960e-02 0.0097931067
## [12,] 0.0002451425 6.410554e-02 1.498205e-12 1.081299e-01 0.0009713337
## [13,] 0.0011839058 3.112729e-10 9.946997e-03 9.207503e-04 0.0971161368
## [14,] 0.0002170825 1.754994e-02 9.373691e-14 2.260795e-02 0.0005161299
## [15,] 0.0049724707 1.719929e-06 8.065684e-03 3.775302e-05 0.1072858266
## [16,] 0.0000000000 1.709817e-02 8.758517e-04 1.094652e-01 0.0019394834
## [17,] 0.0170981653 0.000000e+00 4.299061e-02 1.497329e-03 0.3124203199
## [18,] 0.0008758517 4.299061e-02 0.000000e+00 4.248149e-02 0.0015320582
## [19,] 0.1094651913 1.497329e-03 4.248149e-02 0.000000e+00 0.3027116230
## [20,] 0.0019394834 3.124203e-01 1.532058e-03 3.027116e-01 0.0000000000
## [21,] 0.1693933265 1.463858e-01 2.774369e-01 1.446993e-01 0.5470435732
## [22,] 0.6445814179 5.547493e-01 5.186316e-02 6.556895e-01 0.8579985387
## [23,] 0.2817747334 7.713807e-01 6.754900e-01 7.005500e-01 0.8909780981
## [24,] 0.3215109039 1.688657e-01 9.079266e-01 5.658625e-01 0.7148151662
## [25,] 0.1992179177 6.246838e-01 9.681859e-01 8.916058e-01 0.5778494810
## [26,] 0.6985257161 9.812242e-01 2.874717e-01 9.864706e-01 0.7066986016
## [27,] 0.2646724438 4.166000e-01 5.377620e-01 6.906983e-01 0.6572440070
## [28,] 0.4661421329 6.644153e-01 1.834141e-01 5.620122e-01 0.9168302586
## [29,] 0.2382065073 2.649518e-01 3.724335e-01 9.092432e-01 0.9985967267
## [30,] 0.9439210804 6.165620e-01 4.998088e-02 6.155186e-01 0.8219532157
## [,21] [,22] [,23] [,24] [,25]
## [1,] 0.7718206124 8.538797e-02 5.358152e-02 5.605518e-01 1.868381e-01
## [2,] 0.5248357767 7.695936e-02 1.084108e-01 7.261162e-01 2.660175e-01
## [3,] 0.8213617182 2.611049e-01 1.549420e-01 7.124093e-01 2.631936e-01
## [4,] 0.6139377402 4.825464e-01 1.736191e-01 6.764740e-01 6.126443e-01
## [5,] 0.4225383440 5.604060e-02 1.314766e-01 6.325799e-01 1.895497e-01
## [6,] 0.7561117005 1.926998e-02 2.761958e-02 3.896448e-01 4.795904e-02
## [7,] 0.7563079453 2.883082e-01 1.164382e-01 8.929203e-01 4.345925e-01
## [8,] 0.3185340295 9.505534e-01 7.988963e-01 5.655442e-01 8.246451e-01
## [9,] 0.5785012483 1.252769e-01 1.549538e-01 9.801195e-01 2.721989e-01
## [10,] 0.7819919258 1.757589e-01 1.219640e-01 7.372727e-01 3.634062e-01
## [11,] 0.5205231892 3.255580e-03 2.152283e-01 4.554373e-01 2.939411e-01
## [12,] 0.6577608463 1.691639e-02 3.309055e-01 5.723150e-01 5.758748e-01
## [13,] 0.2467267319 7.251610e-01 7.480777e-01 1.635968e-01 5.192902e-01
## [14,] 0.3833944524 6.376286e-02 5.196893e-01 9.252130e-01 8.510021e-01
## [15,] 0.4538420829 4.973528e-01 1.494924e-01 8.181193e-01 5.910189e-01
## [16,] 0.1693933265 6.445814e-01 2.817747e-01 3.215109e-01 1.992179e-01
## [17,] 0.1463857591 5.547493e-01 7.713807e-01 1.688657e-01 6.246838e-01
## [18,] 0.2774368677 5.186316e-02 6.754900e-01 9.079266e-01 9.681859e-01
## [19,] 0.1446993443 6.556895e-01 7.005500e-01 5.658625e-01 8.916058e-01
## [20,] 0.5470435732 8.579985e-01 8.909781e-01 7.148152e-01 5.778495e-01
## [21,] 0.0000000000 2.468548e-01 6.247771e-03 1.238099e-04 3.494141e-03
## [22,] 0.2468548375 0.000000e+00 4.873221e-04 9.086366e-05 2.985418e-05
## [23,] 0.0062477706 4.873221e-04 0.000000e+00 7.342768e-05 9.360070e-06
## [24,] 0.0001238099 9.086366e-05 7.342768e-05 0.000000e+00 2.749181e-08
## [25,] 0.0034941405 2.985418e-05 9.360070e-06 2.749181e-08 0.000000e+00
## [26,] 0.0316785068 5.034196e-06 1.395881e-05 5.999964e-05 4.250730e-05
## [27,] 0.0022147227 1.235149e-05 5.092240e-08 3.906834e-06 3.085842e-05
## [28,] 0.0537407581 4.301123e-11 5.064473e-06 1.181223e-05 9.142041e-06
## [29,] 0.0510468375 6.566364e-09 3.151473e-05 9.427344e-06 2.519968e-05
## [30,] 0.3886450575 1.983525e-10 3.288311e-03 7.025876e-04 5.149381e-04
## [,26] [,27] [,28] [,29] [,30]
## [1,] 1.035506e-01 2.653185e-01 3.060052e-02 1.717176e-01 6.628234e-02
## [2,] 1.470258e-01 3.916392e-01 9.984162e-02 3.093329e-01 4.416878e-02
## [3,] 2.469688e-01 5.016447e-01 1.431717e-01 4.606382e-01 1.690011e-01
## [4,] 4.909143e-01 7.505951e-01 2.903104e-01 6.061081e-01 3.173599e-01
## [5,] 7.152553e-02 3.029456e-01 4.939281e-02 1.763684e-01 3.012342e-02
## [6,] 4.737378e-02 1.874755e-01 1.875137e-02 1.060368e-01 3.326884e-02
## [7,] 1.564316e-01 2.709774e-01 1.134749e-01 2.022507e-01 1.385428e-01
## [8,] 7.608188e-01 9.016666e-01 6.414055e-01 8.932577e-01 5.420068e-01
## [9,] 1.265031e-01 4.494210e-01 1.196406e-01 3.573646e-01 7.701168e-02
## [10,] 4.100636e-01 4.081194e-01 1.430166e-01 2.676161e-01 8.580533e-02
## [11,] 2.607947e-02 1.258270e-01 1.514030e-02 7.175189e-02 4.360658e-03
## [12,] 7.530589e-02 2.101436e-01 6.190711e-02 1.657445e-01 2.107310e-02
## [13,] 9.977001e-01 4.948236e-01 7.417603e-01 2.706078e-01 7.632926e-01
## [14,] 1.891053e-01 4.244176e-01 1.516430e-01 3.544423e-01 6.689155e-02
## [15,] 5.161689e-01 7.852834e-01 4.720934e-01 8.115429e-01 4.985996e-01
## [16,] 6.985257e-01 2.646724e-01 4.661421e-01 2.382065e-01 9.439211e-01
## [17,] 9.812242e-01 4.166000e-01 6.644153e-01 2.649518e-01 6.165620e-01
## [18,] 2.874717e-01 5.377620e-01 1.834141e-01 3.724335e-01 4.998088e-02
## [19,] 9.864706e-01 6.906983e-01 5.620122e-01 9.092432e-01 6.155186e-01
## [20,] 7.066986e-01 6.572440e-01 9.168303e-01 9.985967e-01 8.219532e-01
## [21,] 3.167851e-02 2.214723e-03 5.374076e-02 5.104684e-02 3.886451e-01
## [22,] 5.034196e-06 1.235149e-05 4.301123e-11 6.566364e-09 1.983525e-10
## [23,] 1.395881e-05 5.092240e-08 5.064473e-06 3.151473e-05 3.288311e-03
## [24,] 5.999964e-05 3.906834e-06 1.181223e-05 9.427344e-06 7.025876e-04
## [25,] 4.250730e-05 3.085842e-05 9.142041e-06 2.519968e-05 5.149381e-04
## [26,] 0.000000e+00 1.276691e-08 4.840914e-08 9.572729e-06 2.098205e-04
## [27,] 1.276691e-08 0.000000e+00 5.241753e-08 7.802251e-07 2.485500e-04
## [28,] 4.840914e-08 5.241753e-08 0.000000e+00 7.990401e-12 3.915216e-08
## [29,] 9.572729e-06 7.802251e-07 7.990401e-12 0.000000e+00 5.698019e-07
## [30,] 2.098205e-04 2.485500e-04 3.915216e-08 5.698019e-07 0.000000e+00
##
## $lowCI
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1.000000000 0.57221780 0.741963663 0.613016108 0.607613707
## [2,] 0.572217798 1.00000000 0.519890076 0.571214246 0.694375190
## [3,] 0.741963663 0.51989008 1.000000000 0.469703444 0.430474504
## [4,] 0.613016108 0.57121425 0.469703444 1.000000000 0.469520623
## [5,] 0.607613707 0.69437519 0.430474504 0.469520623 1.000000000
## [6,] 0.654504443 0.67655068 0.567694665 0.486461630 0.673717448
## [7,] 0.474397410 0.52839469 0.546032573 0.406802756 0.426818506
## [8,] -0.819890213 -0.82555129 -0.796675916 -0.842430517 -0.809293281
## [9,] -0.910889516 -0.91590080 -0.890663612 -0.924396030 -0.921570177
## [10,] -0.825489231 -0.77695579 -0.829791792 -0.804410845 -0.779066839
## [11,] 0.170098622 0.45619253 0.009147698 0.135622992 0.483269726
## [12,] -0.063807442 0.29763180 -0.201867074 -0.009245082 0.214987727
## [13,] 0.171450640 0.35048083 0.077827065 0.237149430 0.303179542
## [14,] -0.024421253 0.33790975 -0.142123110 0.053336652 0.263142865
## [15,] 0.459953137 0.56408874 0.286817835 0.446254457 0.574498065
## [16,] -0.137417375 0.11420036 -0.171170849 -0.101559482 0.045047402
## [17,] -0.735246570 -0.79468498 -0.729891312 -0.748686373 -0.797080157
## [18,] -0.632663667 -0.77957929 -0.542970186 -0.668919514 -0.791865231
## [19,] -0.770253743 -0.77977581 -0.730608257 -0.779067179 -0.785278723
## [20,] -0.503556078 -0.60464332 -0.453898701 -0.584110183 -0.624848733
## [21,] -0.407412129 -0.46101193 -0.397145645 -0.440988810 -0.485700795
## [22,] -0.046230306 -0.03677119 -0.160697429 -0.238422853 -0.008859895
## [23,] -0.005020802 -0.06860563 -0.103970618 -0.115781835 -0.087405006
## [24,] -0.259996118 -0.30078025 -0.297595019 -0.427474465 -0.278421704
## [25,] -0.123550679 -0.16285744 -0.161619450 -0.273442531 -0.125090947
## [26,] -0.598026205 -0.57532584 -0.536223170 -0.468955993 -0.619490719
## [27,] -0.530171535 -0.49366766 -0.466420249 -0.411836770 -0.518469880
## [28,] -0.661395920 -0.60024747 -0.577138487 -0.522303499 -0.638873912
## [29,] -0.564394054 -0.51656532 -0.476236813 -0.442707817 -0.562451118
## [30,] -0.623634355 -0.64436998 -0.565544592 -0.514201882 -0.662092535
## [,6] [,7] [,8] [,9] [,10]
## [1,] 0.654504443 0.474397410 -0.81989021 -0.91088952 -0.82548923
## [2,] 0.676550680 0.528394690 -0.82555129 -0.91590080 -0.77695579
## [3,] 0.567694665 0.546032573 -0.79667592 -0.89066361 -0.82979179
## [4,] 0.486461630 0.406802756 -0.84243052 -0.92439603 -0.80441085
## [5,] 0.673717448 0.426818506 -0.80929328 -0.92157018 -0.77906684
## [6,] 1.000000000 0.398009922 -0.77079417 -0.90333553 -0.77971034
## [7,] 0.398009922 1.000000000 -0.85021191 -0.88310138 -0.84357704
## [8,] -0.770794167 -0.850211909 1.00000000 0.40073111 0.24307710
## [9,] -0.903335532 -0.883101378 0.40073111 1.00000000 0.37510953
## [10,] -0.779710340 -0.843577043 0.24307710 0.37510953 1.00000000
## [11,] 0.271451584 0.167154678 -0.66106568 -0.78882070 -0.62451749
## [12,] 0.042186651 0.009846428 -0.55702685 -0.69822147 -0.47586685
## [13,] 0.146588717 0.079995126 -0.64305206 -0.76457729 -0.56610790
## [14,] 0.081078097 0.078543860 -0.60573454 -0.72259724 -0.47708700
## [15,] 0.495713794 0.244092844 -0.73733403 -0.83506220 -0.71431024
## [16,] -0.194181458 -0.097304374 -0.61757522 -0.59821217 -0.44562284
## [17,] -0.732704318 -0.753859957 0.06808016 0.25184727 0.01309996
## [18,] -0.678065790 -0.679789019 -0.08323565 0.16015431 -0.17587623
## [19,] -0.790928555 -0.721141788 0.03856908 0.16956560 0.02273605
## [20,] -0.465089343 -0.568349260 -0.23964623 -0.13178377 -0.36656349
## [21,] -0.410684947 -0.410643998 -0.18430104 -0.26470552 -0.31349644
## [22,] 0.076260602 -0.172304747 -0.37051473 -0.58601058 -0.56270387
## [23,] 0.048901089 -0.075488279 -0.40179237 -0.57169347 -0.58774530
## [24,] -0.209643693 -0.337728949 -0.26131453 -0.36439691 -0.41462426
## [25,] 0.004354632 -0.224068288 -0.32295248 -0.52796492 -0.50121713
## [26,] -0.640943959 -0.571029931 -0.30872547 -0.08359196 -0.21632648
## [27,] -0.557939316 -0.528354342 -0.33959516 -0.22861080 -0.21569990
## [28,] -0.681995597 -0.592342065 -0.28059944 -0.07812640 -0.09582388
## [29,] -0.596568025 -0.552191193 -0.38232705 -0.19857632 -0.16355394
## [30,] -0.657646782 -0.579358795 -0.25503833 -0.03683252 -0.04667814
## [,11] [,12] [,13] [,14] [,15] [,16]
## [1,] 0.170098622 -0.063807442 0.17145064 -0.02442125 0.4599531 -0.13741737
## [2,] 0.456192527 0.297631805 0.35048083 0.33790975 0.5640887 0.11420036
## [3,] 0.009147698 -0.201867074 0.07782707 -0.14212311 0.2868178 -0.17117085
## [4,] 0.135622992 -0.009245082 0.23714943 0.05333665 0.4462545 -0.10155948
## [5,] 0.483269726 0.214987727 0.30317954 0.26314287 0.5744981 0.04504740
## [6,] 0.271451584 0.042186651 0.14658872 0.08107810 0.4957138 -0.19418146
## [7,] 0.167154678 0.009846428 0.07999513 0.07854386 0.2440928 -0.09730437
## [8,] -0.661065679 -0.557026853 -0.64305206 -0.60573454 -0.7373340 -0.61757522
## [9,] -0.788820697 -0.698221468 -0.76457729 -0.72259724 -0.8350622 -0.59821217
## [10,] -0.624517492 -0.475866848 -0.56610790 -0.47708700 -0.7143102 -0.44562284
## [11,] 1.000000000 0.757779358 0.25144995 0.71422410 0.3791854 0.33948845
## [12,] 0.757779358 1.000000000 0.15887386 0.86244646 0.1553170 0.33689997
## [13,] 0.251449948 0.158873858 1.00000000 0.21014576 0.6463492 0.25504042
## [14,] 0.714224099 0.862446458 0.21014576 1.00000000 0.1645342 0.34277321
## [15,] 0.379185416 0.155316972 0.64634920 0.16453422 1.0000000 0.16949296
## [16,] 0.339488454 0.336899969 0.25504042 0.34277321 0.1694930 1.00000000
## [17,] -0.703042557 -0.625424904 -0.93824575 -0.68461659 -0.8747671 -0.68563892
## [18,] -0.923876520 -0.959082220 -0.70569356 -0.96680951 -0.7129023 -0.77509771
## [19,] -0.703484415 -0.595358702 -0.77392591 -0.67438940 -0.8347183 -0.59459560
## [20,] -0.706239645 -0.772662646 -0.60191672 -0.78698331 -0.5958444 -0.75536802
## [21,] -0.462010544 -0.431481866 -0.53630471 -0.49584375 -0.4778988 -0.56537775
## [22,] 0.195989025 0.085864462 -0.41716627 -0.02005197 -0.2426720 -0.43432192
## [23,] -0.138891719 -0.188976197 -0.30582730 -0.24893773 -0.1003122 -0.52494608
## [24,] -0.230426275 -0.263091947 -0.56786947 -0.34459385 -0.3978156 -0.51299231
## [25,] -0.174607063 -0.264021667 -0.46229664 -0.32870415 -0.2679411 -0.55334914
## [26,] -0.668367794 -0.616637666 -0.35979083 -0.55729167 -0.4630220 -0.29433943
## [27,] -0.585725545 -0.549227106 -0.24195178 -0.48522519 -0.4046148 -0.16226900
## [28,] -0.690333739 -0.627278909 -0.30438232 -0.57319518 -0.4734591 -0.23361900
## [29,] -0.619316863 -0.566939696 -0.16484923 -0.50367497 -0.3991750 -0.15020983
## [30,] -0.732513085 -0.677284477 -0.30928575 -0.62314094 -0.4671376 -0.34854129
## [,17] [,18] [,19] [,20] [,21] [,22]
## [1,] -0.73524657 -0.6326636667 -0.77025374 -0.5035561 -0.40741213 -0.046230306
## [2,] -0.79468498 -0.7795792918 -0.77977581 -0.6046433 -0.46101193 -0.036771191
## [3,] -0.72989131 -0.5429701863 -0.73060826 -0.4538987 -0.39714564 -0.160697429
## [4,] -0.74868637 -0.6689195140 -0.77906718 -0.5841102 -0.44098881 -0.238422853
## [5,] -0.79708016 -0.7918652311 -0.78527872 -0.6248487 -0.48570080 -0.008859895
## [6,] -0.73270432 -0.6780657900 -0.79092856 -0.4650893 -0.41068495 0.076260602
## [7,] -0.75385996 -0.6797890190 -0.72114179 -0.5683493 -0.41064400 -0.172304747
## [8,] 0.06808016 -0.0832356492 0.03856908 -0.2396462 -0.18430104 -0.370514725
## [9,] 0.25184727 0.1601543107 0.16956560 -0.1317838 -0.26470552 -0.586010585
## [10,] 0.01309996 -0.1758762286 0.02273605 -0.3665635 -0.31349644 -0.562703871
## [11,] -0.70304256 -0.9238765204 -0.70348441 -0.7062396 -0.46201054 0.195989025
## [12,] -0.62542490 -0.9590822196 -0.59535870 -0.7726626 -0.43148187 0.085864462
## [13,] -0.93824575 -0.7056935609 -0.77392591 -0.6019167 -0.53630471 -0.417166267
## [14,] -0.68461659 -0.9668095101 -0.67438940 -0.7869833 -0.49584375 -0.020051967
## [15,] -0.87476707 -0.7129023253 -0.83471825 -0.5958444 -0.47789881 -0.242672011
## [16,] -0.68563892 -0.7750977122 -0.59459560 -0.7553680 -0.56537775 -0.434321921
## [17,] 1.00000000 0.0134567728 0.24182424 -0.1819428 -0.09817880 -0.258455271
## [18,] 0.01345677 1.0000000000 0.01443968 0.2405186 -0.16776688 -0.636425294
## [19,] 0.24182424 0.0144396769 1.00000000 -0.1781290 -0.09700553 -0.431927224
## [20,] -0.18194281 0.2405186269 -0.17812896 1.0000000 -0.25639450 -0.389588570
## [21,] -0.09817880 -0.1677668779 -0.09700553 -0.2563945 1.00000000 -0.154255989
## [22,] -0.25845527 -0.6364252940 -0.43192722 -0.3895886 -0.15425599 1.000000000
## [23,] -0.40750366 -0.4276844936 -0.42235751 -0.3373138 0.15472926 0.302550873
## [24,] -0.11287479 -0.3409276266 -0.26139836 -0.2981561 0.36915238 0.383179577
## [25,] -0.27645972 -0.3536333215 -0.38266720 -0.2645360 0.19164275 0.430880181
## [26,] -0.36416788 -0.1719600726 -0.36307965 -0.4210571 -0.65985219 -0.862372204
## [27,] -0.48721010 -0.2538896349 -0.42444637 -0.4315930 -0.75182978 -0.850836111
## [28,] -0.43005358 -0.1215806477 -0.26038249 -0.3774715 -0.63462160 -0.947072345
## [29,] -0.53029006 -0.2038244325 -0.34120753 -0.3605610 -0.63722464 -0.921308110
## [30,] -0.44041414 0.0008802478 -0.27416574 -0.3223613 -0.49445532 -0.940388037
## [,23] [,24] [,25] [,26] [,27] [,28]
## [1,] -0.005020802 -0.2599961 -0.123550679 -0.59802621 -0.5301715 -0.66139592
## [2,] -0.068605631 -0.3007802 -0.162857436 -0.57532584 -0.4936677 -0.60024747
## [3,] -0.103970618 -0.2975950 -0.161619450 -0.53622317 -0.4664202 -0.57713849
## [4,] -0.115781835 -0.4274745 -0.273442531 -0.46895599 -0.4118368 -0.52230350
## [5,] -0.087405006 -0.2784217 -0.125090947 -0.61949072 -0.5184699 -0.63887391
## [6,] 0.048901089 -0.2096437 0.004354632 -0.64094396 -0.5579393 -0.68199560
## [7,] -0.075488279 -0.3377289 -0.224068288 -0.57102993 -0.5283543 -0.59234207
## [8,] -0.401792367 -0.2613145 -0.322952484 -0.30872547 -0.3395952 -0.28059944
## [9,] -0.571693471 -0.3643969 -0.527964920 -0.08359196 -0.2286108 -0.07812640
## [10,] -0.587745304 -0.4146243 -0.501217135 -0.21632648 -0.2156999 -0.09582388
## [11,] -0.138891719 -0.2304263 -0.174607063 -0.66836779 -0.5857255 -0.69033374
## [12,] -0.188976197 -0.2630919 -0.264021667 -0.61663767 -0.5492271 -0.62727891
## [13,] -0.305827297 -0.5678695 -0.462296641 -0.35979083 -0.2419518 -0.30438232
## [14,] -0.248937728 -0.3445938 -0.328704152 -0.55729167 -0.4852252 -0.57319518
## [15,] -0.100312180 -0.3978156 -0.267941062 -0.46302203 -0.4046148 -0.47345909
## [16,] -0.524946083 -0.5129923 -0.553349140 -0.29433943 -0.1622690 -0.23361900
## [17,] -0.407503657 -0.1128748 -0.276459724 -0.36416788 -0.4872101 -0.43005358
## [18,] -0.427684494 -0.3409276 -0.353633321 -0.17196007 -0.2538896 -0.12158065
## [19,] -0.422357506 -0.2613984 -0.382667199 -0.36307965 -0.4244464 -0.26038249
## [20,] -0.337313801 -0.2981561 -0.264535978 -0.42105708 -0.4315930 -0.37747153
## [21,] 0.154729255 0.3691524 0.191642747 -0.65985219 -0.7518298 -0.63462160
## [22,] 0.302550873 0.3831796 0.430880181 -0.86237220 -0.8508361 -0.94707234
## [23,] 1.000000000 0.3926387 0.476386668 -0.84917151 -0.9070083 -0.86229888
## [24,] 0.392638660 1.0000000 0.654156934 -0.82738107 -0.8654288 -0.85143779
## [25,] 0.476386668 0.6541569 1.000000000 -0.83287886 -0.8377860 -0.85483334
## [26,] -0.849171513 -0.8273811 -0.832878856 1.00000000 0.6724462 0.64000862
## [27,] -0.907008318 -0.8654288 -0.837786042 0.67244621 1.0000000 0.63797298
## [28,] -0.862298883 -0.8514378 -0.854833336 0.64000862 0.6379730 1.00000000
## [29,] -0.837469321 -0.8544313 -0.840794680 0.47554298 0.5614714 0.80570104
## [30,] -0.740827517 -0.7801628 -0.787033308 0.34440653 0.3362292 0.64538296
## [,29] [,30]
## [1,] -0.5643941 -0.6236343554
## [2,] -0.5165653 -0.6443699835
## [3,] -0.4762368 -0.5655445919
## [4,] -0.4427078 -0.5142018816
## [5,] -0.5624511 -0.6620925354
## [6,] -0.5965680 -0.6576467819
## [7,] -0.5521912 -0.5793587950
## [8,] -0.3823270 -0.2550383307
## [9,] -0.1985763 -0.0368325204
## [10,] -0.1635539 -0.0466781388
## [11,] -0.6193169 -0.7325130848
## [12,] -0.5669397 -0.6772844769
## [13,] -0.1648492 -0.3092857487
## [14,] -0.5036750 -0.6231409414
## [15,] -0.3991750 -0.4671376204
## [16,] -0.1502098 -0.3485412888
## [17,] -0.5302901 -0.4404141429
## [18,] -0.2038244 0.0008802478
## [19,] -0.3412075 -0.2741657411
## [20,] -0.3605610 -0.3223613421
## [21,] -0.6372246 -0.4944553161
## [22,] -0.9213081 -0.9403880368
## [23,] -0.8374693 -0.7408275169
## [24,] -0.8544313 -0.7801627783
## [25,] -0.8407947 -0.7870333076
## [26,] 0.4755430 0.3444065257
## [27,] 0.5614714 0.3362292388
## [28,] 0.8057010 0.6453829551
## [29,] 1.0000000 0.5711647898
## [30,] 0.5711648 1.0000000000
##
## $uppCI
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 1.00000000 0.88647148 0.93655232 0.89922003 0.897559369 0.911704215
## [2,] 0.88647148 1.00000000 0.86939092 0.88615176 0.923270199 0.918150328
## [3,] 0.93655232 0.86939092 1.00000000 0.85218510 0.838134230 0.885028105
## [4,] 0.89922003 0.88615176 0.85218510 1.00000000 0.852120868 0.858023901
## [5,] 0.89755937 0.92327020 0.83813423 0.85212087 1.000000000 0.917329018
## [6,] 0.91170421 0.91815033 0.88502810 0.85802390 0.917329018 1.000000000
## [7,] 0.85383020 0.87222498 0.87802992 0.82938552 0.836796587 0.826082158
## [8,] -0.38173749 -0.39660417 -0.32305619 -0.44230815 -0.354504993 -0.261661316
## [9,] -0.65174889 -0.66880760 -0.58546412 -0.69833274 -0.688425359 -0.626520824
## [10,] -0.39643996 -0.27591311 -0.40788961 -0.34221224 -0.280847155 -0.282356432
## [11,] 0.72879793 0.84740729 0.64315645 0.71181544 0.856919149 0.775037160
## [12,] 0.59830070 0.78616461 0.50030456 0.63224368 0.749925776 0.662132921
## [13,] 0.72945021 0.80770185 0.68174935 0.75996912 0.788482598 0.717291155
## [14,] 0.62304356 0.80268710 0.54504064 0.66836256 0.771439168 0.683496511
## [15,] 0.84874353 0.88387304 0.78160640 0.84385203 0.887196818 0.861206866
## [16,] 0.54840553 0.70091211 0.52376778 0.57333689 0.663739472 0.506277600
## [17,] -0.18355816 -0.31818754 -0.17236613 -0.21229052 -0.324047799 -0.178227177
## [18,] 0.00854516 -0.28204887 0.14500324 -0.05434102 -0.311334805 -0.071014713
## [19,] -0.26042182 -0.28251012 -0.17385619 -0.28084795 -0.295520253 -0.309069445
## [20,] 0.19769399 0.05390398 0.25877099 0.08550233 0.021466852 0.245486916
## [21,] 0.31121135 0.25035819 0.32223135 0.27376821 0.220300738 0.307657227
## [22,] 0.60950111 0.61542217 0.53153914 0.47094911 0.632474856 0.680905036
## [23,] 0.63477274 0.59519760 0.57169877 0.56359566 0.582845815 0.665894651
## [24,] 0.45285519 0.41696549 0.41985142 0.28910387 0.436921949 0.494191998
## [25,] 0.55819359 0.52994588 0.53085964 0.44127234 0.557115649 0.640337234
## [26,] 0.06423312 0.09862126 0.15430857 0.24083405 0.030203080 -0.005383688
## [27,] 0.16255191 0.21030666 0.24388908 0.30640162 0.178221901 0.123914303
## [28,] -0.04087768 0.06078152 0.09593322 0.17312683 -0.001878245 -0.078284496
## [29,] 0.11462656 0.18073935 0.23198334 0.27179112 0.117434799 0.066490378
## [30,] 0.02345558 -0.01121988 0.11295849 0.18385067 -0.042114868 -0.034251741
## [,7] [,8] [,9] [,10] [,11] [,12]
## [1,] 0.85383020 -0.381737486 -0.65174889 -0.39643996 0.72879793 0.59830070
## [2,] 0.87222498 -0.396604170 -0.66880760 -0.27591311 0.84740729 0.78616461
## [3,] 0.87802992 -0.323056191 -0.58546412 -0.40788961 0.64315645 0.50030456
## [4,] 0.82938552 -0.442308146 -0.69833274 -0.34221224 0.71181544 0.63224368
## [5,] 0.83679659 -0.354504993 -0.68842536 -0.28084716 0.85691915 0.74992578
## [6,] 0.82608216 -0.261661316 -0.62652082 -0.28235643 0.77503716 0.66213292
## [7,] 1.00000000 -0.464101761 -0.56168654 -0.44548985 0.72737411 0.64356600
## [8,] -0.46410176 1.000000000 0.82710763 0.76261379 -0.04029184 0.12521768
## [9,] -0.56168654 0.827107625 1.00000000 0.81733844 -0.30399149 -0.10899646
## [10,] -0.44548985 0.762613791 0.81733844 1.00000000 0.02200982 0.23243592
## [11,] 0.72737411 -0.040291838 -0.30399149 0.02200982 1.00000000 0.94084620
## [12,] 0.64356600 0.125217681 -0.10899646 0.23243592 0.94084620 1.00000000
## [13,] 0.68291527 -0.008969705 -0.24750327 0.11214039 0.76632002 0.72334313
## [14,] 0.68213516 0.052186953 -0.15735026 0.23094213 0.92887744 0.96785410
## [15,] 0.76306523 -0.187959851 -0.42209801 -0.14060166 0.81890972 0.72159979
## [16,] 0.57621470 0.033302397 0.06394476 0.26842462 0.80332050 0.80228142
## [17,] -0.22360377 0.676469572 0.76649505 0.64546826 -0.11834376 0.02052149
## [18,] -0.07419461 0.585612206 0.72396896 0.52023829 -0.69650483 -0.82743359
## [19,] -0.15438496 0.660093161 0.72854049 0.65105658 -0.11920566 0.06835727
## [20,] 0.10887613 0.469938761 0.55240491 0.35394198 -0.12460006 -0.26595977
## [21,] 0.30770182 0.513858896 0.44882567 0.40529811 0.24916847 0.28459444
## [22,] 0.52291943 0.349936060 0.08263330 0.11707009 0.74111495 0.68605629
## [23,] 0.59071159 0.317267617 0.10397840 0.08000469 0.54735367 0.51028516
## [24,] 0.38239652 0.451730040 0.35612738 0.30335256 0.47750773 0.45020957
## [25,] 0.48266671 0.396467486 0.16553383 0.20069842 0.52119264 0.44941260
## [26,] 0.10495280 0.409703197 0.58537640 0.48888302 -0.05334608 0.03481483
## [27,] 0.16500850 0.380595339 0.47898583 0.48938302 0.08306433 0.13626370
## [28,] 0.07299404 0.435008645 0.58898111 0.57721208 -0.09392490 0.01747165
## [29,] 0.13208594 0.337801039 0.50287024 0.52943108 0.03048490 0.11093069
## [30,] 0.09262721 0.457066005 0.61538402 0.60921896 -0.17782748 -0.06957700
## [,13] [,14] [,15] [,16] [,17] [,18]
## [1,] 0.729450210 0.62304356 0.84874353 0.54840553 -0.18355816 0.008545160
## [2,] 0.807701854 0.80268710 0.88387304 0.70091211 -0.31818754 -0.282048870
## [3,] 0.681749348 0.54504064 0.78160640 0.52376778 -0.17236613 0.145003244
## [4,] 0.759969124 0.66836256 0.84385203 0.57333689 -0.21229052 -0.054341023
## [5,] 0.788482598 0.77143917 0.88719682 0.66373947 -0.32404780 -0.311334805
## [6,] 0.717291155 0.68349651 0.86120687 0.50627760 -0.17822718 -0.071014713
## [7,] 0.682915269 0.68213516 0.76306523 0.57621470 -0.22360377 -0.074194609
## [8,] -0.008969705 0.05218695 -0.18795985 0.03330240 0.67646957 0.585612206
## [9,] -0.247503275 -0.15735026 -0.42209801 0.06394476 0.76649505 0.723968957
## [10,] 0.112140391 0.23094213 -0.14060166 0.26842462 0.64546826 0.520238291
## [11,] 0.766320024 0.92887744 0.81890972 0.80332050 -0.11834376 -0.696504826
## [12,] 0.723343125 0.96785410 0.72159979 0.80228142 0.02052149 -0.827433591
## [13,] 1.000000000 0.74769815 0.90928717 0.76789891 -0.74817533 -0.123528157
## [14,] 0.747698145 1.00000000 0.72610268 0.80463502 -0.08316905 -0.858223405
## [15,] 0.909287174 0.72610268 1.00000000 0.72850540 -0.53608229 -0.137788434
## [16,] 0.767898912 0.80463502 0.72850540 1.00000000 -0.08508215 -0.271592061
## [17,] -0.748175325 -0.08316905 -0.53608229 -0.08508215 1.00000000 0.645676401
## [18,] -0.123528157 -0.85822340 -0.13778843 -0.27159206 0.64567640 1.000000000
## [19,] -0.268877377 -0.06427162 -0.42116453 0.06953292 0.76205626 0.646249282
## [20,] 0.058177258 -0.29958748 0.06760803 -0.22692861 0.51565240 0.761474437
## [21,] 0.154196837 0.20755102 0.22994640 0.11320062 0.57562467 0.526306307
## [22,] 0.300559162 0.62571080 0.46743184 0.28137928 0.45416730 0.002248161
## [23,] 0.412362851 0.46220401 0.57418219 0.16959290 0.31111223 0.288868321
## [24,] 0.109576113 0.37574375 0.32151815 0.18543762 0.56560225 0.379305945
## [25,] 0.248827227 0.39103032 0.44604031 0.13044722 0.43864017 0.366868861
## [26,] 0.360747426 0.12483966 0.24796122 0.42278619 0.35635794 0.523177450
## [27,] 0.468029609 0.22089271 0.31423329 0.53038041 0.21841869 0.458037098
## [28,] 0.413684346 0.10176838 0.23537389 0.47489855 0.28620530 0.559568942
## [29,] 0.528472349 0.19754092 0.32006836 0.53920596 0.16239138 0.498772605
## [30,] 0.409187618 0.02426216 0.24302623 0.37188436 0.27442780 0.638282879
## [,19] [,20] [,21] [,22] [,23] [,24]
## [1,] -0.26042182 0.19769399 0.3112113545 0.609501109 0.63477274 0.4528552
## [2,] -0.28251012 0.05390398 0.2503581948 0.615422171 0.59519760 0.4169655
## [3,] -0.17385619 0.25877099 0.3222313516 0.531539136 0.57169877 0.4198514
## [4,] -0.28084795 0.08550233 0.2737682062 0.470949111 0.56359566 0.2891039
## [5,] -0.29552025 0.02146685 0.2203007376 0.632474856 0.58284582 0.4369219
## [6,] -0.30906944 0.24548692 0.3076572272 0.680905036 0.66589465 0.4941920
## [7,] -0.15438496 0.10887613 0.3077018207 0.522919427 0.59071159 0.3823965
## [8,] 0.66009316 0.46993876 0.5138588960 0.349936060 0.31726762 0.4517300
## [9,] 0.72854049 0.55240491 0.4488256685 0.082633299 0.10397840 0.3561274
## [10,] 0.65105658 0.35394198 0.4052981124 0.117070095 0.08000469 0.3033526
## [11,] -0.11920566 -0.12460006 0.2491684704 0.741114949 0.54735367 0.4775077
## [12,] 0.06835727 -0.26595977 0.2845944378 0.686056288 0.51028516 0.4502096
## [13,] -0.26887738 0.05817726 0.1541968367 0.300559162 0.41236285 0.1095761
## [14,] -0.06427162 -0.29958748 0.2075510211 0.625710805 0.46220401 0.3757437
## [15,] -0.42116453 0.06760803 0.2299464041 0.467431844 0.57418219 0.3215181
## [16,] 0.06953292 -0.22692861 0.1132006155 0.281379285 0.16959290 0.1854376
## [17,] 0.76205626 0.51565240 0.5756246661 0.454167297 0.31111223 0.5656023
## [18,] 0.64624928 0.76147444 0.5263063073 0.002248161 0.28886832 0.3793059
## [19,] 1.00000000 0.51854006 0.5764161819 0.284091322 0.29481601 0.4516584
## [20,] 0.51854006 1.00000000 0.4559173252 0.330220389 0.38279646 0.4193441
## [21,] 0.57641618 0.45591733 1.0000000000 0.536261544 0.72131104 0.8150300
## [22,] 0.28409132 0.33022039 0.5362615442 1.000000000 0.78822061 0.8204431
## [23,] 0.29481601 0.38279646 0.7213110371 0.788220614 1.00000000 0.8240497
## [24,] 0.45165842 0.41934407 0.8150300222 0.820443125 0.82404966 1.0000000
## [25,] 0.33744801 0.44897124 0.7390725802 0.838282356 0.85452511 0.9116016
## [26,] 0.35745224 0.29625957 -0.0381427906 -0.499122045 -0.46116056 -0.4014580
## [27,] 0.29249036 0.28446898 -0.2191472182 -0.465870474 -0.63871482 -0.5081153
## [28,] 0.45252569 0.34281835 0.0052738886 -0.781100735 -0.49890727 -0.4675783
## [29,] 0.37903473 0.35997736 0.0009034924 -0.687510945 -0.42865553 -0.4761179
## [30,] 0.44064253 0.39702346 0.2093105165 -0.756081492 -0.19537606 -0.2834191
## [,25] [,26] [,27] [,28] [,29]
## [1,] 0.5581936 0.064233117 0.16255191 -0.040877681 0.1146265574
## [2,] 0.5299459 0.098621265 0.21030666 0.060781525 0.1807393461
## [3,] 0.5308596 0.154308570 0.24388908 0.095933223 0.2319833387
## [4,] 0.4412723 0.240834049 0.30640162 0.173126831 0.2717911221
## [5,] 0.5571156 0.030203080 0.17822190 -0.001878245 0.1174347990
## [6,] 0.6403372 -0.005383688 0.12391430 -0.078284496 0.0664903777
## [7,] 0.4826667 0.104952796 0.16500850 0.072994043 0.1320859362
## [8,] 0.3964675 0.409703197 0.38059534 0.435008645 0.3378010390
## [9,] 0.1655338 0.585376398 0.47898583 0.588981112 0.5028702437
## [10,] 0.2006984 0.488883020 0.48938302 0.577212083 0.5294310810
## [11,] 0.5211926 -0.053346079 0.08306433 -0.093924904 0.0304849003
## [12,] 0.4494126 0.034814826 0.13626370 0.017471649 0.1109306916
## [13,] 0.2488272 0.360747426 0.46802961 0.413684346 0.5284723492
## [14,] 0.3910303 0.124839660 0.22089271 0.101768380 0.1975409164
## [15,] 0.4460403 0.247961219 0.31423329 0.235373889 0.3200683601
## [16,] 0.1304472 0.422786189 0.53038041 0.474898549 0.5392059578
## [17,] 0.4386402 0.356357938 0.21841869 0.286205303 0.1623913824
## [18,] 0.3668689 0.523177450 0.45803710 0.559568942 0.4987726046
## [19,] 0.3374480 0.357452238 0.29249036 0.452525694 0.3790347316
## [20,] 0.4489712 0.296259570 0.28446898 0.342818349 0.3599773624
## [21,] 0.7390726 -0.038142791 -0.21914722 0.005273889 0.0009034924
## [22,] 0.8382824 -0.499122045 -0.46587047 -0.781100735 -0.6875109455
## [23,] 0.8545251 -0.461160560 -0.63871482 -0.498907272 -0.4286555251
## [24,] 0.9116016 -0.401457991 -0.50811530 -0.467578278 -0.4761178713
## [25,] 1.0000000 -0.416187254 -0.42952156 -0.477270258 -0.4377859330
## [26,] -0.4161873 1.000000000 0.91695983 0.907395627 0.8542305509
## [27,] -0.4295216 0.916959830 1.00000000 0.906786040 0.8830321749
## [28,] -0.4772703 0.907395627 0.90678604 1.000000000 0.9535073380
## [29,] -0.4377859 0.854230551 0.88303217 0.953507338 1.0000000000
## [30,] -0.2997070 0.805286974 0.80201171 0.908999621 0.8861359967
## [,30]
## [1,] 0.02345558
## [2,] -0.01121988
## [3,] 0.11295849
## [4,] 0.18385067
## [5,] -0.04211487
## [6,] -0.03425174
## [7,] 0.09262721
## [8,] 0.45706601
## [9,] 0.61538402
## [10,] 0.60921896
## [11,] -0.17782748
## [12,] -0.06957700
## [13,] 0.40918762
## [14,] 0.02426216
## [15,] 0.24302623
## [16,] 0.37188436
## [17,] 0.27442780
## [18,] 0.63828288
## [19,] 0.44064253
## [20,] 0.39702346
## [21,] 0.20931052
## [22,] -0.75608149
## [23,] -0.19537606
## [24,] -0.28341906
## [25,] -0.29970704
## [26,] 0.80528697
## [27,] 0.80201171
## [28,] 0.90899962
## [29,] 0.88613600
## [30,] 1.00000000corrplot::corrplot(perstdMatrix_AEO, p.mat = res_max_AEO$p, type="lower", sig.level = .05)
#Showing p-value for non-significant results
corrplot(perstdMatrix_AEO, p.mat = res_max_AEO$p, type="lower",insig = "p-value")
Step 2: Check if data is suitable - look at the relevant Statistics
checking for multicollinearity, inspect determinant > 0.00001 1. Barteltt’s test: 2. KMO Measure of Sampling Adequacy 3. Determinant test
# Bartlett’s test: test variables are correlated
#Compares the correlation matrix with a matrix of zero correlations (technically called the identity matrix, #which consists of all zeros except the 1’s along the diagonal).
cat("\n *** Barteltt's test result for Stduent Personality data (A,E,O) *** \n")##
## *** Barteltt's test result for Stduent Personality data (A,E,O) ***psych::cortest.bartlett(std_AEO)## R was not square, finding R from data## $chisq
## [1] 3978.985
##
## $p.value
## [1] 0
##
## $df
## [1] 435cat("\n *** Barteltt's test result for Stduent Personality Correlation Matrix (A,E,O) *** \n")##
## *** Barteltt's test result for Stduent Personality Correlation Matrix (A,E,O) ***psych::cortest.bartlett(perstdMatrix_AEO, n=nrow(std_AEO))## $chisq
## [1] 3978.985
##
## $p.value
## [1] 0
##
## $df
## [1] 435# KMO test:the proportion of variance in your variables that might be caused by an underlying factor.
# High values close to 1 -> PCA/FA might be useful
# Values over 0.8 or over are considered strong
# Anything less than 0.5 suggests that PCA/FA won’t be useful
# KMO reference:
# 0.00 to 0.49 unacceptable.
# 0.50 to 0.59 miserable.
# 0.60 to 0.69 mediocre.
# 0.70 to 0.79 middling.
# 0.80 to 0.89 meritorious.
# 0.90 to 1.00 marvellous.
cat("\n *** KMO test result for Stduent Personality data (A,E,O) *** \n")##
## *** KMO test result for Stduent Personality data (A,E,O) ***REdaS::KMOS(std_AEO)##
## Kaiser-Meyer-Olkin Statistics
##
## Call: REdaS::KMOS(x = std_AEO)
##
## Measures of Sampling Adequacy (MSA):
## A1 A2 A3 A4 A5 A6 A7 A8
## 0.8754913 0.9100732 0.8287707 0.8450145 0.8760763 0.8744542 0.8133833 0.6757972
## A9 A10 E1 E2 E3 E4 E5 E6
## 0.8404421 0.7426791 0.8815091 0.8186950 0.7713451 0.8324620 0.8370609 0.8218991
## E7 E8 E9 E10 O1 O2 O3 O4
## 0.6594875 0.7629369 0.6834679 0.7154004 0.7322455 0.8119045 0.7779430 0.7920795
## O5 O6 O7 O8 O9 O10
## 0.8216486 0.7868623 0.7807232 0.7991763 0.7916679 0.8379533
##
## KMO-Criterion: 0.816615cat("\n *** KMO test result for Stduent Personality Correlation Matrix (A,E,O) *** \n")##
## *** KMO test result for Stduent Personality Correlation Matrix (A,E,O) ***psych::KMO(std_AEO)## Kaiser-Meyer-Olkin factor adequacy
## Call: psych::KMO(r = std_AEO)
## Overall MSA = 0.82
## MSA for each item =
## A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 E1 E2 E3 E4 E5 E6
## 0.88 0.91 0.83 0.85 0.88 0.87 0.81 0.68 0.84 0.74 0.88 0.82 0.77 0.83 0.84 0.82
## E7 E8 E9 E10 O1 O2 O3 O4 O5 O6 O7 O8 O9 O10
## 0.66 0.76 0.68 0.72 0.73 0.81 0.78 0.79 0.82 0.79 0.78 0.80 0.79 0.84#the result is 0.82, PCA/FA is userful# Determinant test
#Indicator of multicollinearity
#Should be greater than 0.00001 = 1.0e-5
cat("\n *** Determinant test result for Stduent Personality data (A,E,O) *** \n")##
## *** Determinant test result for Stduent Personality data (A,E,O) ***det(cor(std_AEO))## [1] 2.146319e-05cat("\n *** Determinant test result for Stduent Personality Correlation Matrix (A,E,O) *** \n")##
## *** Determinant test result for Stduent Personality Correlation Matrix (A,E,O) ***det(perstdMatrix_AEO)## [1] 2.146319e-05#the result is greater than 0.00001Step 3: Dimension Reduction by PCA (Principal Components Analysis)
## Principal Components Analysis
## Call: principal(r = std_AEO, nfactors = length(std_AEO), rotate = "none")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11 PC12
## A1 0.62 0.05 0.08 -0.36 0.14 0.07 -0.08 0.00 -0.08 -0.06 -0.10 0.33
## A2 0.72 0.15 0.13 -0.07 0.14 0.02 0.09 0.05 0.03 0.07 0.07 -0.03
## A3 0.54 0.11 0.14 -0.42 0.22 0.00 0.06 -0.09 0.09 -0.24 0.20 0.29
## A4 0.54 0.16 -0.04 -0.29 0.12 -0.13 -0.29 0.28 0.00 0.16 -0.34 0.00
## A5 0.66 0.05 -0.11 -0.11 0.01 0.12 0.00 -0.03 -0.33 -0.16 0.00 -0.21
## A6 0.65 0.02 0.18 -0.25 0.09 0.27 -0.02 0.23 -0.10 0.05 0.18 -0.02
## A7 0.49 0.05 -0.13 -0.26 0.16 -0.35 0.09 -0.14 0.34 -0.02 0.40 0.09
## A8 -0.22 -0.08 0.44 0.29 -0.19 0.31 -0.22 0.11 0.34 -0.40 0.03 0.04
## A9 -0.47 0.00 0.43 0.29 -0.07 0.11 -0.02 -0.27 0.13 0.28 0.11 0.22
## A10 -0.19 0.10 0.41 0.39 -0.10 0.07 -0.08 0.26 -0.43 -0.04 0.22 0.32
## E1 0.64 -0.01 -0.03 0.45 0.02 0.10 0.18 -0.12 -0.01 0.10 -0.09 -0.01
## E2 0.55 0.01 0.00 0.65 0.08 -0.09 0.06 0.12 0.11 0.06 -0.03 -0.01
## E3 0.51 0.38 0.14 0.08 -0.51 0.06 0.09 -0.01 0.09 -0.10 -0.16 0.08
## E4 0.54 0.09 -0.08 0.60 0.06 -0.10 -0.03 0.17 0.08 0.09 0.21 0.00
## E5 0.63 0.26 0.18 -0.06 -0.33 0.13 -0.10 -0.14 -0.02 0.17 -0.23 -0.01
## E6 0.38 0.33 0.15 0.37 0.08 -0.13 0.18 -0.48 -0.15 0.01 -0.16 0.17
## E7 -0.27 -0.25 0.35 0.11 0.63 0.01 -0.14 0.09 -0.10 0.25 -0.12 0.13
## E8 -0.36 0.01 0.46 -0.54 -0.08 0.05 0.06 -0.20 -0.09 -0.01 -0.11 0.15
## E9 -0.20 -0.08 0.39 0.13 0.28 -0.29 0.42 0.17 0.06 -0.37 -0.34 0.01
## E10 -0.10 -0.07 0.30 -0.31 -0.08 0.32 0.60 0.21 0.14 0.37 0.07 -0.09
## O1 0.13 -0.20 0.57 -0.02 -0.03 -0.42 -0.09 0.01 0.03 0.05 -0.02 -0.20
## O2 0.36 -0.58 0.14 0.17 0.18 0.39 0.08 0.02 0.13 -0.06 -0.09 0.06
## O3 0.34 -0.40 0.38 -0.12 -0.28 -0.22 -0.15 0.15 0.25 0.10 -0.13 0.10
## O4 0.23 -0.47 0.51 0.03 0.03 -0.10 -0.07 -0.29 -0.16 0.02 0.12 -0.23
## O5 0.31 -0.40 0.50 -0.08 -0.03 0.08 -0.08 -0.05 -0.11 -0.12 0.15 -0.34
## O6 -0.12 0.59 0.18 0.00 0.28 0.17 -0.29 -0.13 0.28 0.14 -0.09 -0.15
## O7 -0.06 0.67 0.14 0.02 0.27 0.33 -0.08 -0.07 0.06 -0.15 0.02 -0.10
## O8 -0.17 0.75 0.26 0.02 0.09 -0.08 0.04 0.05 0.02 -0.03 0.03 -0.21
## O9 -0.08 0.71 0.22 0.00 0.01 -0.07 0.21 0.12 -0.09 -0.03 0.02 -0.11
## O10 -0.14 0.57 0.34 -0.07 -0.16 -0.26 -0.08 0.17 -0.06 0.09 0.17 0.10
## PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20 PC21 PC22 PC23 PC24
## A1 -0.14 -0.17 0.11 -0.16 0.26 0.06 0.08 0.05 0.07 -0.10 0.12 -0.18
## A2 0.12 0.22 -0.08 -0.08 -0.31 0.11 -0.27 0.01 0.18 0.13 -0.03 -0.21
## A3 -0.20 -0.08 -0.07 -0.17 -0.04 -0.04 0.05 -0.15 -0.01 0.08 -0.19 0.02
## A4 -0.19 0.21 -0.12 0.14 0.12 0.05 -0.08 0.10 0.13 -0.02 -0.24 0.12
## A5 0.26 -0.23 0.22 -0.04 -0.03 0.17 0.04 0.28 0.07 0.16 0.00 0.05
## A6 0.17 -0.14 0.01 0.01 -0.13 -0.14 -0.21 -0.10 -0.28 -0.12 0.00 0.10
## A7 0.15 0.12 0.11 0.23 -0.03 0.01 0.19 0.11 0.07 -0.13 0.06 0.07
## A8 -0.12 -0.25 -0.10 0.15 -0.13 0.18 -0.01 0.01 0.09 0.03 -0.05 -0.01
## A9 0.17 -0.05 0.08 -0.19 0.09 -0.07 -0.16 0.25 0.10 -0.10 -0.24 -0.07
## A10 0.01 0.31 0.17 -0.01 -0.07 0.09 0.19 -0.06 0.00 -0.03 -0.08 0.08
## E1 -0.02 -0.14 0.04 0.22 0.02 -0.21 0.15 0.00 0.05 0.05 -0.19 0.10
## E2 -0.02 0.02 -0.01 0.02 0.01 -0.01 -0.08 -0.09 0.00 -0.14 0.13 -0.22
## E3 -0.12 0.19 0.11 -0.03 -0.04 -0.07 0.06 0.11 0.06 0.07 0.22 -0.01
## E4 -0.06 0.08 -0.05 -0.09 0.11 0.01 -0.05 0.03 -0.05 0.12 0.04 0.07
## E5 0.16 -0.12 0.09 0.06 -0.07 -0.02 0.10 -0.23 0.03 -0.22 -0.04 -0.06
## E6 -0.08 -0.03 -0.22 0.12 -0.03 0.21 -0.03 0.01 -0.22 0.10 -0.01 0.06
## E7 0.03 -0.18 -0.08 0.12 -0.16 0.04 0.16 0.07 0.05 0.00 0.19 -0.05
## E8 0.07 0.21 -0.06 0.19 -0.14 -0.16 -0.07 0.03 0.00 0.07 0.10 0.00
## E9 0.26 0.06 0.18 -0.04 0.13 0.00 -0.07 -0.08 -0.02 -0.03 -0.09 0.00
## E10 -0.18 -0.03 0.06 0.05 0.09 0.25 0.07 -0.02 -0.01 0.05 -0.01 0.01
## O1 -0.38 -0.11 0.34 0.01 -0.22 -0.08 -0.05 0.12 -0.14 -0.02 -0.04 -0.01
## O2 0.01 0.07 0.00 0.01 0.03 -0.29 -0.01 0.05 0.12 0.09 0.10 0.16
## O3 0.31 -0.01 -0.21 -0.15 0.03 0.15 0.08 0.10 -0.16 0.00 0.06 0.15
## O4 -0.11 0.03 -0.02 -0.15 0.16 0.10 -0.14 -0.20 0.22 -0.06 0.14 0.21
## O5 0.05 0.18 -0.22 0.11 0.21 -0.08 0.20 0.05 -0.10 0.02 -0.11 -0.28
## O6 0.09 0.13 0.23 -0.20 0.04 -0.02 0.16 -0.15 -0.13 0.25 0.01 0.00
## O7 -0.06 0.16 0.07 0.17 0.17 0.11 -0.16 0.15 -0.12 -0.22 0.08 0.08
## O8 0.12 -0.06 -0.13 -0.02 -0.12 0.02 0.15 -0.08 0.25 -0.09 -0.04 0.08
## O9 -0.12 -0.10 -0.29 -0.28 -0.03 -0.22 0.09 0.18 -0.02 -0.08 0.06 0.04
## O10 0.10 -0.24 0.01 0.27 0.28 -0.11 -0.17 -0.08 0.06 0.23 0.08 -0.03
## PC25 PC26 PC27 PC28 PC29 PC30 h2 u2 com
## A1 0.08 0.22 -0.14 -0.08 -0.03 0.00 1 -4.4e-16 5.2
## A2 0.01 -0.04 -0.18 -0.11 0.04 -0.09 1 -2.9e-15 3.5
## A3 0.04 -0.23 0.10 0.16 -0.05 0.01 1 -2.2e-15 7.1
## A4 -0.09 0.04 0.13 -0.03 0.02 0.05 1 -1.6e-15 7.8
## A5 0.00 -0.05 0.10 0.06 0.02 0.13 1 -1.8e-15 4.6
## A6 -0.05 0.17 0.14 -0.07 -0.08 -0.07 1 -4.4e-16 5.0
## A7 -0.10 0.05 0.05 -0.09 0.08 0.02 1 3.3e-16 8.0
## A8 0.00 0.09 0.05 -0.10 0.09 0.03 1 2.2e-15 9.7
## A9 -0.04 0.02 0.10 0.04 -0.03 -0.02 1 1.1e-16 8.9
## A10 -0.05 -0.03 -0.06 -0.07 0.00 0.05 1 4.4e-16 8.6
## E1 0.27 -0.05 -0.06 -0.20 -0.06 -0.06 1 -2.2e-16 4.5
## E2 0.02 -0.10 0.15 -0.02 -0.13 0.27 1 -6.7e-16 3.6
## E3 -0.04 -0.03 0.20 0.03 -0.10 -0.21 1 1.2e-15 6.0
## E4 0.20 0.18 0.02 0.25 0.20 -0.03 1 -4.4e-16 4.4
## E5 -0.06 -0.08 -0.06 0.13 0.23 0.00 1 0.0e+00 5.3
## E6 -0.18 0.11 -0.03 0.00 -0.03 0.02 1 0.0e+00 8.6
## E7 0.01 -0.09 0.12 0.06 0.04 -0.14 1 1.4e-15 5.3
## E8 0.25 0.11 0.08 0.05 0.06 0.19 1 -8.9e-16 6.4
## E9 0.00 0.03 0.05 0.00 0.07 -0.06 1 -2.2e-16 9.2
## E10 -0.01 0.00 0.02 0.02 0.01 0.04 1 -6.7e-16 5.5
## O1 -0.01 0.01 -0.13 0.06 -0.03 0.02 1 1.3e-15 5.6
## O2 -0.24 0.01 -0.18 0.10 -0.02 0.09 1 1.1e-15 6.0
## O3 0.11 -0.12 -0.13 -0.01 -0.10 0.02 1 3.3e-16 11.7
## O4 0.03 -0.03 0.09 -0.11 0.03 -0.03 1 1.1e-15 7.2
## O5 -0.05 0.02 0.02 0.04 -0.01 -0.06 1 3.3e-16 7.8
## O6 -0.02 0.03 0.04 -0.12 0.01 0.06 1 1.1e-16 6.5
## O7 0.11 -0.18 -0.12 0.05 -0.02 -0.04 1 1.1e-16 4.5
## O8 0.02 0.18 -0.08 0.17 -0.23 0.01 1 1.1e-16 3.0
## O9 -0.05 -0.06 0.00 -0.15 0.17 0.06 1 1.4e-15 3.6
## O10 -0.09 -0.10 -0.06 -0.01 -0.01 0.00 1 1.1e-16 6.9
##
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11
## SS loadings 5.44 3.58 2.59 2.45 1.36 1.21 0.99 0.92 0.87 0.83 0.82
## Proportion Var 0.18 0.12 0.09 0.08 0.05 0.04 0.03 0.03 0.03 0.03 0.03
## Cumulative Var 0.18 0.30 0.39 0.47 0.51 0.55 0.59 0.62 0.65 0.68 0.70
## Proportion Explained 0.18 0.12 0.09 0.08 0.05 0.04 0.03 0.03 0.03 0.03 0.03
## Cumulative Proportion 0.18 0.30 0.39 0.47 0.51 0.55 0.59 0.62 0.65 0.68 0.70
## PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20 PC21 PC22
## SS loadings 0.80 0.73 0.70 0.64 0.60 0.56 0.51 0.50 0.45 0.43 0.41
## Proportion Var 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01
## Cumulative Var 0.73 0.75 0.78 0.80 0.82 0.84 0.85 0.87 0.89 0.90 0.91
## Proportion Explained 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01
## Cumulative Proportion 0.73 0.75 0.78 0.80 0.82 0.84 0.85 0.87 0.89 0.90 0.91
## PC23 PC24 PC25 PC26 PC27 PC28 PC29 PC30
## SS loadings 0.40 0.38 0.34 0.33 0.33 0.30 0.26 0.25
## Proportion Var 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
## Cumulative Var 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00
## Proportion Explained 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
## Cumulative Proportion 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00
##
## Mean item complexity = 6.3
## Test of the hypothesis that 30 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0
## with the empirical chi square 0 with prob < NA
##
## Fit based upon off diagonal values = 1
#Factor Analysis
#Principal Axis Factoring fm=pa
factsol <- fa(perstdMatrix_AEO, nfactors=3, obs=NA, n.iter=1, rotate="varimax", fm="pa")
psych::print.psych(factsol,cut=0.3, sort=TRUE)## Factor Analysis using method = pa
## Call: fa(r = perstdMatrix_AEO, nfactors = 3, n.iter = 1, rotate = "varimax",
## fm = "pa", obs = NA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## item PA1 PA2 PA3 h2 u2 com
## A2 2 0.72 0.522 0.48 1.0
## E5 15 0.66 0.450 0.55 1.1
## A6 6 0.64 0.428 0.57 1.1
## A1 1 0.60 0.369 0.63 1.0
## A5 5 0.59 0.394 0.61 1.3
## A3 3 0.55 0.313 0.69 1.1
## E1 11 0.55 0.396 0.60 1.6
## E3 13 0.55 0.360 0.64 1.4
## A4 4 0.51 0.270 0.73 1.1
## E2 12 0.46 0.296 0.70 1.8
## E4 14 0.45 -0.33 0.322 0.68 1.9
## A7 7 0.43 0.202 0.80 1.2
## E6 16 0.39 0.202 0.80 1.7
## A9 9 -0.35 0.33 0.251 0.75 2.4
## O8 28 0.78 0.616 0.38 1.0
## O9 29 0.69 0.482 0.52 1.0
## O7 27 0.60 0.374 0.63 1.0
## O10 30 0.58 0.367 0.63 1.2
## O2 22 -0.56 0.398 0.60 1.5
## O6 26 0.55 0.303 0.70 1.0
## E8 18 0.58 0.425 0.58 1.5
## O5 25 0.31 -0.33 0.48 0.438 0.56 2.6
## O4 24 -0.37 0.48 0.416 0.58 2.3
## O1 21 0.45 0.248 0.75 1.4
## O3 23 0.31 -0.34 0.36 0.342 0.66 3.0
## E7 17 0.32 0.156 0.84 2.0
## E10 20 0.30 0.094 0.91 1.0
## A8 8 0.107 0.89 1.5
## E9 19 0.100 0.90 1.4
## A10 10 0.074 0.93 2.3
##
## PA1 PA2 PA3
## SS loadings 4.61 3.06 2.04
## Proportion Var 0.15 0.10 0.07
## Cumulative Var 0.15 0.26 0.32
## Proportion Explained 0.47 0.32 0.21
## Cumulative Proportion 0.47 0.79 1.00
##
## Mean item complexity = 1.5
## Test of the hypothesis that 3 factors are sufficient.
##
## The degrees of freedom for the null model are 435 and the objective function was 10.75
## The degrees of freedom for the model are 348 and the objective function was 3.83
##
## The root mean square of the residuals (RMSR) is 0.08
## The df corrected root mean square of the residuals is 0.09
##
## Fit based upon off diagonal values = 0.86
## Measures of factor score adequacy
## PA1 PA2 PA3
## Correlation of (regression) scores with factors 0.94 0.92 0.87
## Multiple R square of scores with factors 0.88 0.85 0.75
## Minimum correlation of possible factor scores 0.76 0.69 0.50fa.graph(factsol)## digraph Factor {
## rankdir=RL;
## size="8,6";
## node [fontname="Helvetica" fontsize=14 shape=box, width=2];
## edge [fontname="Helvetica" fontsize=10];
## V1 [label = "A1"];
## V2 [label = "A2"];
## V3 [label = "A3"];
## V4 [label = "A4"];
## V5 [label = "A5"];
## V6 [label = "A6"];
## V7 [label = "A7"];
## V8 [label = "A8"];
## V9 [label = "A9"];
## V10 [label = "A10"];
## V11 [label = "E1"];
## V12 [label = "E2"];
## V13 [label = "E3"];
## V14 [label = "E4"];
## V15 [label = "E5"];
## V16 [label = "E6"];
## V17 [label = "E7"];
## V18 [label = "E8"];
## V19 [label = "E9"];
## V20 [label = "E10"];
## V21 [label = "O1"];
## V22 [label = "O2"];
## V23 [label = "O3"];
## V24 [label = "O4"];
## V25 [label = "O5"];
## V26 [label = "O6"];
## V27 [label = "O7"];
## V28 [label = "O8"];
## V29 [label = "O9"];
## V30 [label = "O10"];
## node [shape=ellipse, width ="1"];
## PA1-> V1 [ label = 0.6 ];
## PA1-> V2 [ label = 0.7 ];
## PA1-> V3 [ label = 0.5 ];
## PA1-> V4 [ label = 0.5 ];
## PA1-> V5 [ label = 0.6 ];
## PA1-> V6 [ label = 0.6 ];
## PA1-> V7 [ label = 0.4 ];
## PA1-> V9 [ label = -0.3 ];
## PA1-> V11 [ label = 0.5 ];
## PA1-> V12 [ label = 0.5 ];
## PA1-> V13 [ label = 0.5 ];
## PA1-> V14 [ label = 0.5 ];
## PA1-> V15 [ label = 0.7 ];
## PA1-> V16 [ label = 0.4 ];
## PA2-> V22 [ label = -0.6 ];
## PA2-> V26 [ label = 0.5 ];
## PA2-> V27 [ label = 0.6 ];
## PA2-> V28 [ label = 0.8 ];
## PA2-> V29 [ label = 0.7 ];
## PA2-> V30 [ label = 0.6 ];
## PA3-> V17 [ label = 0.3 ];
## PA3-> V18 [ label = 0.6 ];
## PA3-> V20 [ label = 0.3 ];
## PA3-> V21 [ label = 0.5 ];
## PA3-> V23 [ label = 0.4 ];
## PA3-> V24 [ label = 0.5 ];
## PA3-> V25 [ label = 0.5 ];
## { rank=same;
## V1;V2;V3;V4;V5;V6;V7;V8;V9;V10;V11;V12;V13;V14;V15;V16;V17;V18;V19;V20;V21;V22;V23;V24;V25;V26;V27;V28;V29;V30;}{ rank=same;
## PA1;PA2;PA3;}}fa.sort(factsol$loading)##
## Loadings:
## PA1 PA2 PA3
## A2 0.722
## E5 0.659 0.125
## A6 0.643
## A1 0.604
## A5 0.590 -0.111 -0.186
## A3 0.549 0.102
## E1 0.549 -0.181 -0.249
## E3 0.547 0.234
## A4 0.512
## E2 0.457 -0.139 -0.260
## E4 0.454 -0.328
## A7 0.427 -0.120
## E6 0.389 0.196 -0.108
## A9 -0.350 0.151 0.326
## O8 0.781
## O9 0.687
## O7 0.605
## O10 0.577 0.179
## O2 0.246 -0.564 0.138
## O6 0.549
## E8 -0.211 0.196 0.585
## O5 0.315 -0.328 0.481
## O4 0.218 -0.371 0.480
## O1 0.179 0.455
## O3 0.312 -0.340 0.359
## E7 -0.218 0.316
## E10 0.304
## A8 -0.146 0.290
## E9 -0.130 0.286
## A10 0.154 0.204
##
## PA1 PA2 PA3
## SS loadings 4.611 3.065 2.038
## Proportion Var 0.154 0.102 0.068
## Cumulative Var 0.154 0.256 0.324fa.diagram(factsol)#create a diagram showing the factors and how the manifest variables load
plot(factsol$values, type = "b") #scree plot
#Cattell (1966) suggests using the ‘point of inflexion’ of the scree plot to decide how many factors to extractStep 4: Decide which components to retain by PCA
cat("\n ****** the variance explained by each component ****** \n")##
## ****** the variance explained by each component ******pca$Vaccounted## PC1 PC2 PC3 PC4 PC5
## SS loadings 5.4418988 3.5848171 2.59159171 2.45164176 1.35903681
## Proportion Var 0.1813966 0.1194939 0.08638639 0.08172139 0.04530123
## Cumulative Var 0.1813966 0.3008905 0.38727692 0.46899831 0.51429954
## Proportion Explained 0.1813966 0.1194939 0.08638639 0.08172139 0.04530123
## Cumulative Proportion 0.1813966 0.3008905 0.38727692 0.46899831 0.51429954
## PC6 PC7 PC8 PC9 PC10
## SS loadings 1.21130561 0.99123094 0.92278265 0.8672491 0.83366725
## Proportion Var 0.04037685 0.03304103 0.03075942 0.0289083 0.02778891
## Cumulative Var 0.55467640 0.58771743 0.61847685 0.6473852 0.67517406
## Proportion Explained 0.04037685 0.03304103 0.03075942 0.0289083 0.02778891
## Cumulative Proportion 0.55467640 0.58771743 0.61847685 0.6473852 0.67517406
## PC11 PC12 PC13 PC14 PC15
## SS loadings 0.82287232 0.80443707 0.73430158 0.69520832 0.63503972
## Proportion Var 0.02742908 0.02681457 0.02447672 0.02317361 0.02116799
## Cumulative Var 0.70260314 0.72941771 0.75389443 0.77706804 0.79823603
## Proportion Explained 0.02742908 0.02681457 0.02447672 0.02317361 0.02116799
## Cumulative Proportion 0.70260314 0.72941771 0.75389443 0.77706804 0.79823603
## PC16 PC17 PC18 PC19 PC20
## SS loadings 0.60482207 0.56338838 0.50817416 0.4969471 0.45273052
## Proportion Var 0.02016074 0.01877961 0.01693914 0.0165649 0.01509102
## Cumulative Var 0.81839676 0.83717638 0.85411552 0.8706804 0.88577143
## Proportion Explained 0.02016074 0.01877961 0.01693914 0.0165649 0.01509102
## Cumulative Proportion 0.81839676 0.83717638 0.85411552 0.8706804 0.88577143
## PC21 PC22 PC23 PC24 PC25
## SS loadings 0.43323733 0.40770152 0.40206968 0.38016343 0.34276023
## Proportion Var 0.01444124 0.01359005 0.01340232 0.01267211 0.01142534
## Cumulative Var 0.90021268 0.91380273 0.92720505 0.93987717 0.95130251
## Proportion Explained 0.01444124 0.01359005 0.01340232 0.01267211 0.01142534
## Cumulative Proportion 0.90021268 0.91380273 0.92720505 0.93987717 0.95130251
## PC26 PC27 PC28 PC29 PC30
## SS loadings 0.33023591 0.32555046 0.30056280 0.257070196 0.247505423
## Proportion Var 0.01100786 0.01085168 0.01001876 0.008569007 0.008250181
## Cumulative Var 0.96231037 0.97316205 0.98318081 0.991749819 1.000000000
## Proportion Explained 0.01100786 0.01085168 0.01001876 0.008569007 0.008250181
## Cumulative Proportion 0.96231037 0.97316205 0.98318081 0.991749819 1.000000000cat("\n *********** the Eigenvalues ************ \n")##
## *********** the Eigenvalues ************pca$values## [1] 5.4418988 3.5848171 2.5915917 2.4516418 1.3590368 1.2113056 0.9912309
## [8] 0.9227826 0.8672491 0.8336672 0.8228723 0.8044371 0.7343016 0.6952083
## [15] 0.6350397 0.6048221 0.5633884 0.5081742 0.4969471 0.4527305 0.4332373
## [22] 0.4077015 0.4020697 0.3801634 0.3427602 0.3302359 0.3255505 0.3005628
## [29] 0.2570702 0.2475054#eigenvalues = the variance of a component or factor (>1) Kaiser (1960)
#for Extracting the factors
pcf=princomp(std_AEO)
factoextra::get_eigenvalue(pcf)## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 6.4935692 17.3162573 17.31626
## Dim.2 5.2769732 14.0719877 31.38825
## Dim.3 3.3011752 8.8031708 40.19142
## Dim.4 3.0632926 8.1688146 48.36023
## Dim.5 1.6803381 4.4809206 52.84115
## Dim.6 1.4822533 3.9526921 56.79384
## Dim.7 1.3354577 3.5612356 60.35508
## Dim.8 1.2901079 3.4403021 63.79538
## Dim.9 1.0359151 2.7624520 66.55783
## Dim.10 0.9899518 2.6398825 69.19772
## Dim.11 0.9338883 2.4903794 71.68809
## Dim.12 0.8798536 2.3462861 74.03438
## Dim.13 0.8342527 2.2246832 76.25906
## Dim.14 0.8118244 2.1648741 78.42394
## Dim.15 0.7994347 2.1318347 80.55577
## Dim.16 0.7271965 1.9391988 82.49497
## Dim.17 0.6872631 1.8327092 84.32768
## Dim.18 0.6750484 1.8001366 86.12782
## Dim.19 0.5851450 1.5603932 87.68821
## Dim.20 0.5618526 1.4982798 89.18649
## Dim.21 0.5188680 1.3836539 90.57014
## Dim.22 0.5124710 1.3665950 91.93674
## Dim.23 0.4712769 1.2567437 93.19348
## Dim.24 0.4589876 1.2239722 94.41746
## Dim.25 0.4166374 1.1110377 95.52849
## Dim.26 0.4026666 1.0737821 96.60228
## Dim.27 0.3539550 0.9438840 97.54616
## Dim.28 0.3373023 0.8994765 98.44564
## Dim.29 0.3041572 0.8110892 99.25672
## Dim.30 0.2787271 0.7432753 100.00000
cat("\n *********** PCA: Above the level of 0.3 ************ \n")##
## *********** PCA: Above the level of 0.3 ************psych::print.psych(pca, cut = 0.3, sort = TRUE)## Principal Components Analysis
## Call: principal(r = std_AEO, nfactors = length(std_AEO), rotate = "none")
## Standardized loadings (pattern matrix) based upon correlation matrix
## item PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11
## A2 2 0.72
## A5 5 0.66 -0.33
## A6 6 0.65
## E1 11 0.64 0.45
## E5 15 0.63 -0.33
## A1 1 0.62 -0.36
## A3 3 0.54 -0.42
## A4 4 0.54 -0.34
## E3 13 0.51 0.38 -0.51
## A7 7 0.49 -0.35 0.34 0.40
## A9 9 -0.47 0.43
## O8 28 0.75
## O9 29 0.71
## O7 27 0.67 0.33
## O6 26 0.59
## O2 22 0.36 -0.58 0.39
## O10 30 0.57 0.34
## O3 23 0.34 -0.40 0.38
## O1 21 0.57 -0.42
## O4 24 -0.47 0.51
## O5 25 0.31 -0.40 0.50
## A8 8 0.44 0.31 0.34 -0.40
## E2 12 0.55 0.65
## E4 14 0.54 0.60
## E8 18 -0.36 0.46 -0.54
## E7 17 0.35 0.63
## E10 20 -0.31 0.32 0.60 0.37
## E9 19 0.39 0.42 -0.37 -0.34
## E6 16 0.38 0.33 0.37 -0.48
## A10 10 0.41 0.39 -0.43
## PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20 PC21 PC22 PC23
## A2 -0.31
## A5
## A6
## E1
## E5
## A1 0.33
## A3
## A4
## E3
## A7
## A9
## O8
## O9
## O7
## O6
## O2
## O10
## O3 0.31
## O1 -0.38 0.34
## O4
## O5 -0.34
## A8
## E2
## E4
## E8
## E7
## E10
## E9
## E6
## A10 0.32 0.31
## PC24 PC25 PC26 PC27 PC28 PC29 PC30 h2 u2 com
## A2 1 -2.9e-15 3.5
## A5 1 -1.8e-15 4.6
## A6 1 -4.4e-16 5.0
## E1 1 -2.2e-16 4.5
## E5 1 0.0e+00 5.3
## A1 1 -4.4e-16 5.2
## A3 1 -2.2e-15 7.1
## A4 1 -1.6e-15 7.8
## E3 1 1.2e-15 6.0
## A7 1 3.3e-16 8.0
## A9 1 1.1e-16 8.9
## O8 1 1.1e-16 3.0
## O9 1 1.4e-15 3.6
## O7 1 1.1e-16 4.5
## O6 1 1.1e-16 6.5
## O2 1 1.1e-15 6.0
## O10 1 1.1e-16 6.9
## O3 1 3.3e-16 11.7
## O1 1 1.3e-15 5.6
## O4 1 1.1e-15 7.2
## O5 1 3.3e-16 7.8
## A8 1 2.2e-15 9.7
## E2 1 -6.7e-16 3.6
## E4 1 -4.4e-16 4.4
## E8 1 -8.9e-16 6.4
## E7 1 1.4e-15 5.3
## E10 1 -6.7e-16 5.5
## E9 1 -2.2e-16 9.2
## E6 1 0.0e+00 8.6
## A10 1 4.4e-16 8.6
##
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11
## SS loadings 5.44 3.58 2.59 2.45 1.36 1.21 0.99 0.92 0.87 0.83 0.82
## Proportion Var 0.18 0.12 0.09 0.08 0.05 0.04 0.03 0.03 0.03 0.03 0.03
## Cumulative Var 0.18 0.30 0.39 0.47 0.51 0.55 0.59 0.62 0.65 0.68 0.70
## Proportion Explained 0.18 0.12 0.09 0.08 0.05 0.04 0.03 0.03 0.03 0.03 0.03
## Cumulative Proportion 0.18 0.30 0.39 0.47 0.51 0.55 0.59 0.62 0.65 0.68 0.70
## PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20 PC21 PC22
## SS loadings 0.80 0.73 0.70 0.64 0.60 0.56 0.51 0.50 0.45 0.43 0.41
## Proportion Var 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01
## Cumulative Var 0.73 0.75 0.78 0.80 0.82 0.84 0.85 0.87 0.89 0.90 0.91
## Proportion Explained 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01
## Cumulative Proportion 0.73 0.75 0.78 0.80 0.82 0.84 0.85 0.87 0.89 0.90 0.91
## PC23 PC24 PC25 PC26 PC27 PC28 PC29 PC30
## SS loadings 0.40 0.38 0.34 0.33 0.33 0.30 0.26 0.25
## Proportion Var 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
## Cumulative Var 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00
## Proportion Explained 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
## Cumulative Proportion 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00
##
## Mean item complexity = 6.3
## Test of the hypothesis that 30 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0
## with the empirical chi square 0 with prob < NA
##
## Fit based upon off diagonal values = 1#create a diagram showing the components and how the manifest variables load
fa.diagram(pca) 
cat("\n *********** Variables on to components ************ \n")##
## *********** Variables on to components ************fa.sort(pca$loading)##
## Loadings:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10
## A2 0.718 0.145 0.131 0.140
## A5 0.658 -0.115 -0.106 0.123 -0.327 -0.156
## A6 0.648 0.177 -0.245 0.266 0.225 -0.101
## E1 0.642 0.445 0.101 0.177 -0.120 0.102
## E5 0.630 0.260 0.183 -0.330 0.134 -0.104 -0.138 0.169
## A1 0.622 -0.364 0.139
## A3 0.544 0.107 0.143 -0.420 0.225 -0.243
## A4 0.542 0.164 -0.286 0.119 -0.130 -0.290 0.282 0.163
## E3 0.514 0.384 0.142 -0.506
## A7 0.493 -0.126 -0.256 0.160 -0.352 -0.142 0.345
## A9 -0.466 0.428 0.289 0.110 -0.266 0.132 0.279
## O8 -0.175 0.749 0.258
## O9 0.709 0.222 0.206 0.121
## O7 0.666 0.143 0.274 0.334 -0.154
## O6 -0.124 0.589 0.181 0.283 0.175 -0.287 -0.130 0.283 0.138
## O2 0.360 -0.579 0.138 0.167 0.182 0.390 0.131
## O10 -0.136 0.569 0.339 -0.163 -0.257 0.167
## O3 0.338 -0.397 0.376 -0.116 -0.278 -0.215 -0.145 0.151 0.246
## O1 0.128 -0.199 0.571 -0.421
## O4 0.226 -0.473 0.510 -0.101 -0.293 -0.158
## O5 0.311 -0.405 0.505 -0.109 -0.123
## A8 -0.224 0.438 0.294 -0.187 0.306 -0.216 0.114 0.340 -0.395
## E2 0.550 0.648 0.125 0.110
## E4 0.545 0.598 0.167
## E8 -0.361 0.459 -0.537 -0.199
## E7 -0.268 -0.246 0.350 0.114 0.625 -0.144 -0.105 0.252
## E10 -0.102 0.295 -0.312 0.318 0.597 0.211 0.135 0.371
## E9 -0.203 0.388 0.130 0.285 -0.294 0.417 0.174 -0.365
## E6 0.379 0.332 0.153 0.370 -0.129 0.182 -0.478 -0.146
## A10 -0.186 0.411 0.394 -0.105 0.264 -0.429
## PC11 PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20
## A2 0.123 0.217 -0.309 0.109 -0.267
## A5 -0.210 0.259 -0.229 0.217 0.171 0.283
## A6 0.184 0.172 -0.142 -0.129 -0.139 -0.209
## E1 -0.140 0.216 -0.209 0.149
## E5 -0.227 0.164 -0.116 -0.235
## A1 0.332 -0.142 -0.166 0.108 -0.163 0.264
## A3 0.196 0.286 -0.199 -0.172 -0.154
## A4 -0.337 -0.187 0.208 -0.119 0.136 0.116
## E3 -0.157 -0.119 0.192 0.114 0.107
## A7 0.395 0.154 0.117 0.109 0.230 0.186 0.109
## A9 0.114 0.215 0.167 -0.191 -0.164 0.252
## O8 -0.212 0.123 -0.127 -0.119 0.148
## O9 -0.110 -0.122 -0.102 -0.293 -0.283 -0.225 0.181
## O7 -0.100 0.165 0.175 0.165 0.109 -0.161 0.154
## O6 -0.153 0.134 0.229 -0.200 0.156 -0.147
## O2 -0.293
## O10 0.175 0.104 0.103 -0.244 0.267 0.281 -0.114 -0.174
## O3 -0.126 0.100 0.306 -0.214 -0.153 0.152
## O1 -0.204 -0.378 -0.110 0.343 -0.217 0.121
## O4 0.125 -0.234 -0.105 -0.151 0.158 0.101 -0.138 -0.195
## O5 0.148 -0.336 0.176 -0.217 0.113 0.215 0.204
## A8 -0.123 -0.249 0.150 -0.134 0.182
## E2
## E4 0.213 0.110
## E8 -0.107 0.151 0.210 0.189 -0.136 -0.160
## E7 -0.119 0.133 -0.180 0.124 -0.163 0.163
## E10 -0.181 0.254
## E9 -0.344 0.264 0.181 0.125
## E6 -0.155 0.171 -0.223 0.118 0.213
## A10 0.222 0.318 0.305 0.168 0.194
## PC21 PC22 PC23 PC24 PC25 PC26 PC27 PC28 PC29 PC30
## A2 0.175 0.133 -0.205 -0.181 -0.107
## A5 0.159 0.100 0.133
## A6 -0.280 -0.123 0.105 0.171 0.140
## E1 -0.193 0.101 0.273 -0.195
## E5 -0.222 0.134 0.233
## A1 0.121 -0.180 0.221 -0.140
## A3 -0.191 -0.232 0.161
## A4 0.131 -0.240 0.122 0.131
## E3 0.220 0.205 -0.101 -0.211
## A7 -0.134 -0.102
## A9 -0.236 0.103
## O8 0.246 0.179 0.173 -0.229
## O9 -0.152 0.173
## O7 -0.119 -0.219 0.109 -0.182 -0.124
## O6 -0.127 0.248 -0.122
## O2 0.120 0.104 0.158 -0.238 -0.181 0.105
## O10 0.234
## O3 -0.164 0.154 0.109 -0.118 -0.129
## O1 -0.135 -0.128
## O4 0.218 0.138 0.213 -0.110
## O5 -0.105 -0.110 -0.281
## A8 -0.101
## E2 -0.143 0.133 -0.221 -0.101 0.148 -0.132 0.272
## E4 0.121 0.195 0.180 0.246 0.195
## E8 0.100 0.249 0.107 0.192
## E7 0.189 0.122 -0.143
## E10
## E9
## E6 -0.217 -0.184 0.110
## A10
##
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10
## SS loadings 5.442 3.585 2.592 2.452 1.359 1.211 0.991 0.923 0.867 0.834
## Proportion Var 0.181 0.119 0.086 0.082 0.045 0.040 0.033 0.031 0.029 0.028
## Cumulative Var 0.181 0.301 0.387 0.469 0.514 0.555 0.588 0.618 0.647 0.675
## PC11 PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20
## SS loadings 0.823 0.804 0.734 0.695 0.635 0.605 0.563 0.508 0.497 0.453
## Proportion Var 0.027 0.027 0.024 0.023 0.021 0.020 0.019 0.017 0.017 0.015
## Cumulative Var 0.703 0.729 0.754 0.777 0.798 0.818 0.837 0.854 0.871 0.886
## PC21 PC22 PC23 PC24 PC25 PC26 PC27 PC28 PC29 PC30
## SS loadings 0.433 0.408 0.402 0.380 0.343 0.330 0.326 0.301 0.257 0.248
## Proportion Var 0.014 0.014 0.013 0.013 0.011 0.011 0.011 0.010 0.009 0.008
## Cumulative Var 0.900 0.914 0.927 0.940 0.951 0.962 0.973 0.983 0.992 1.000# The communalities of variables across components (will be one for PCA since all the variance is used)
# In the initial PCA because we have as many components/factors as manifest variables this will be 1
pca$communality ## A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 E1 E2 E3 E4 E5 E6 E7 E8 E9 E10
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## O1 O2 O3 O4 O5 O6 O7 O8 O9 O10
## 1 1 1 1 1 1 1 1 1 1#Visualize contribution of variables to each component
var <- factoextra::get_pca_var(pcf)
corrplot::corrplot(var$contrib, is.corr=FALSE)
# Contributions of variables to PC1
factoextra::fviz_contrib(pcf, choice = "var", axes = 1, top = 10)
# Contributions of variables to PC2
factoextra::fviz_contrib(pcf, choice = "var", axes = 2, top = 10)
# Contributions of variables to PC3
factoextra::fviz_contrib(pcf, choice = "var", axes = 3, top = 10)
## Step 5: Apply rotation The aim of rotation is to clarify the data structure. The factor patterns define decreasing amounts of variation in the data. Each pattern may involve all or most of the variables and the variables may have moderate or high loadings for several factor patterns. Geometric Rotation
#Apply rotation to try to refine the component structure
pc_rotat <- principal(std_AEO, nfactors = 3, rotate = "varimax") #Extracting 3 factors
cat("\n\n ****************** Output the components **************** \n")##
##
## ****************** Output the components ****************psych::print.psych(pc_rotat, cut = 0.3, sort = TRUE)## Principal Components Analysis
## Call: principal(r = std_AEO, nfactors = 3, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
## item RC1 RC2 RC3 h2 u2 com
## A2 2 0.74 0.55 0.45 1.0
## E5 15 0.69 0.50 0.50 1.1
## A6 6 0.66 0.45 0.55 1.1
## A1 1 0.63 0.40 0.60 1.0
## A5 5 0.63 0.45 0.55 1.3
## E1 11 0.61 0.41 0.59 1.2
## E3 13 0.59 0.43 0.57 1.5
## A3 3 0.57 0.33 0.67 1.0
## A4 4 0.55 0.32 0.68 1.2
## E2 12 0.54 0.30 0.70 1.1
## E4 14 0.53 0.31 0.69 1.2
## A7 7 0.46 0.26 0.74 1.4
## E6 16 0.45 0.28 0.72 1.6
## O8 28 0.81 0.66 0.34 1.0
## O9 29 0.74 0.56 0.44 1.0
## O7 27 0.68 0.47 0.53 1.0
## O10 30 0.65 0.46 0.54 1.2
## O6 26 0.63 0.39 0.61 1.0
## O2 22 -0.59 0.48 0.52 1.8
## O1 21 0.58 0.38 0.62 1.3
## O4 24 -0.38 0.58 0.53 0.47 2.1
## O5 25 0.32 -0.34 0.55 0.52 0.48 2.4
## E8 18 0.48 0.34 0.66 1.9
## A9 9 -0.37 0.47 0.40 0.60 2.3
## A8 8 0.47 0.25 0.75 1.3
## E7 17 0.43 0.26 0.74 1.7
## E9 19 0.42 0.20 0.80 1.3
## O3 23 0.33 -0.36 0.42 0.41 0.59 2.9
## A10 10 0.39 0.21 0.79 1.7
## E10 20 0.31 0.10 0.90 1.1
##
## RC1 RC2 RC3
## SS loadings 5.30 3.61 2.71
## Proportion Var 0.18 0.12 0.09
## Cumulative Var 0.18 0.30 0.39
## Proportion Explained 0.46 0.31 0.23
## Cumulative Proportion 0.46 0.77 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 3 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.08
## with the empirical chi square 2387.19 with prob < 2.7e-300
##
## Fit based upon off diagonal values = 0.83cat("\n\n ****************** Output the communalities **************** \n")##
##
## ****************** Output the communalities ****************pc_rotat$communality## A1 A2 A3 A4 A5 A6 A7 A8
## 0.3965544 0.5541820 0.3276494 0.3221578 0.4486197 0.4517483 0.2610561 0.2479507
## A9 A10 E1 E2 E3 E4 E5 E6
## 0.4006096 0.2131236 0.4132195 0.3028360 0.4316967 0.3111398 0.4974551 0.2775750
## E7 E8 E9 E10 O1 O2 O3 O4
## 0.2555838 0.3405504 0.1986758 0.1021134 0.3816605 0.4839259 0.4132861 0.5341659
## O5 O6 O7 O8 O9 O10
## 0.5151607 0.3946487 0.4673077 0.6582340 0.5581462 0.4572746Step 6: Dimension reduction and Decide which factores/compenents to retain
#Factor Analysis - the default here is principal axis factoring fm=pa
#If we know our data going in is normally distributed we use maximum likelihood
facsol <- psych::fa(perstdMatrix_AEO, nfactors=3, obs=NA, n.iter=1, rotate="varimax", fm="pa")
plot(facsol$values, type = "b") #scree plot
cat("\n *** the Variance accounted for each factor/component *** \n")##
## *** the Variance accounted for each factor/component ***facsol$Vaccounted #(3 factors)## PA1 PA2 PA3
## SS loadings 4.6114062 3.0648476 2.03807042
## Proportion Var 0.1537135 0.1021616 0.06793568
## Cumulative Var 0.1537135 0.2558751 0.32381081
## Proportion Explained 0.4747017 0.3154978 0.20980053
## Cumulative Proportion 0.4747017 0.7901995 1.00000000cat("\n\n ******* Output the Eigenvalues ******* \n")##
##
## ******* Output the Eigenvalues *******facsol$values ## [1] 4.80707315 3.00062414 1.90662696 1.74086885 0.65994818 0.49529984
## [7] 0.23427859 0.21763862 0.19986766 0.12553273 0.09895981 0.08148037
## [13] 0.02936610 0.00574592 -0.02519957 -0.05011261 -0.10392919 -0.14227435
## [19] -0.17595295 -0.19383450 -0.19650206 -0.22449309 -0.26887744 -0.29953683
## [25] -0.30854426 -0.32222712 -0.34825614 -0.35616921 -0.41605302 -0.45632223cat("\n\n ******* the components with loadings ******* \n")##
##
## ******* the components with loadings *******psych::print.psych(facsol,cut=0.3, sort=TRUE)## Factor Analysis using method = pa
## Call: psych::fa(r = perstdMatrix_AEO, nfactors = 3, n.iter = 1, rotate = "varimax",
## fm = "pa", obs = NA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## item PA1 PA2 PA3 h2 u2 com
## A2 2 0.72 0.522 0.48 1.0
## E5 15 0.66 0.450 0.55 1.1
## A6 6 0.64 0.428 0.57 1.1
## A1 1 0.60 0.369 0.63 1.0
## A5 5 0.59 0.394 0.61 1.3
## A3 3 0.55 0.313 0.69 1.1
## E1 11 0.55 0.396 0.60 1.6
## E3 13 0.55 0.360 0.64 1.4
## A4 4 0.51 0.270 0.73 1.1
## E2 12 0.46 0.296 0.70 1.8
## E4 14 0.45 -0.33 0.322 0.68 1.9
## A7 7 0.43 0.202 0.80 1.2
## E6 16 0.39 0.202 0.80 1.7
## A9 9 -0.35 0.33 0.251 0.75 2.4
## O8 28 0.78 0.616 0.38 1.0
## O9 29 0.69 0.482 0.52 1.0
## O7 27 0.60 0.374 0.63 1.0
## O10 30 0.58 0.367 0.63 1.2
## O2 22 -0.56 0.398 0.60 1.5
## O6 26 0.55 0.303 0.70 1.0
## E8 18 0.58 0.425 0.58 1.5
## O5 25 0.31 -0.33 0.48 0.438 0.56 2.6
## O4 24 -0.37 0.48 0.416 0.58 2.3
## O1 21 0.45 0.248 0.75 1.4
## O3 23 0.31 -0.34 0.36 0.342 0.66 3.0
## E7 17 0.32 0.156 0.84 2.0
## E10 20 0.30 0.094 0.91 1.0
## A8 8 0.107 0.89 1.5
## E9 19 0.100 0.90 1.4
## A10 10 0.074 0.93 2.3
##
## PA1 PA2 PA3
## SS loadings 4.61 3.06 2.04
## Proportion Var 0.15 0.10 0.07
## Cumulative Var 0.15 0.26 0.32
## Proportion Explained 0.47 0.32 0.21
## Cumulative Proportion 0.47 0.79 1.00
##
## Mean item complexity = 1.5
## Test of the hypothesis that 3 factors are sufficient.
##
## The degrees of freedom for the null model are 435 and the objective function was 10.75
## The degrees of freedom for the model are 348 and the objective function was 3.83
##
## The root mean square of the residuals (RMSR) is 0.08
## The df corrected root mean square of the residuals is 0.09
##
## Fit based upon off diagonal values = 0.86
## Measures of factor score adequacy
## PA1 PA2 PA3
## Correlation of (regression) scores with factors 0.94 0.92 0.87
## Multiple R square of scores with factors 0.88 0.85 0.75
## Minimum correlation of possible factor scores 0.76 0.69 0.50cat("\n\n ******* sorted list of loadings ******* \n")##
##
## ******* sorted list of loadings *******fa.sort(facsol$loading)##
## Loadings:
## PA1 PA2 PA3
## A2 0.722
## E5 0.659 0.125
## A6 0.643
## A1 0.604
## A5 0.590 -0.111 -0.186
## A3 0.549 0.102
## E1 0.549 -0.181 -0.249
## E3 0.547 0.234
## A4 0.512
## E2 0.457 -0.139 -0.260
## E4 0.454 -0.328
## A7 0.427 -0.120
## E6 0.389 0.196 -0.108
## A9 -0.350 0.151 0.326
## O8 0.781
## O9 0.687
## O7 0.605
## O10 0.577 0.179
## O2 0.246 -0.564 0.138
## O6 0.549
## E8 -0.211 0.196 0.585
## O5 0.315 -0.328 0.481
## O4 0.218 -0.371 0.480
## O1 0.179 0.455
## O3 0.312 -0.340 0.359
## E7 -0.218 0.316
## E10 0.304
## A8 -0.146 0.290
## E9 -0.130 0.286
## A10 0.154 0.204
##
## PA1 PA2 PA3
## SS loadings 4.611 3.065 2.038
## Proportion Var 0.154 0.102 0.068
## Cumulative Var 0.154 0.256 0.324#create a diagram showing the factors and how the manifest variables load
fa.diagram(facsol) ## Step 7: Rotation for 3 factors
#Apply rotation to try to refine the component structure
facsolrot <- principal(perstdMatrix_AEO, rotate = "varimax")
cat("\n\n ******* Output the components ******* \n")##
##
## ******* Output the components *******psych::print.psych(facsolrot, cut = 0.3, sort = TRUE)## Principal Components Analysis
## Call: principal(r = perstdMatrix_AEO, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
## V PC1 h2 u2 com
## A2 2 0.72 0.5158 0.48 1
## A5 5 0.66 0.4327 0.57 1
## A6 6 0.65 0.4200 0.58 1
## E1 11 0.64 0.4120 0.59 1
## E5 15 0.63 0.3967 0.60 1
## A1 1 0.62 0.3867 0.61 1
## E2 12 0.55 0.3026 0.70 1
## E4 14 0.54 0.2968 0.70 1
## A3 3 0.54 0.2957 0.70 1
## A4 4 0.54 0.2934 0.71 1
## E3 13 0.51 0.2644 0.74 1
## A7 7 0.49 0.2429 0.76 1
## A9 9 -0.47 0.2172 0.78 1
## E6 16 0.38 0.1436 0.86 1
## E8 18 -0.36 0.1302 0.87 1
## O2 22 0.36 0.1299 0.87 1
## O3 23 0.34 0.1146 0.89 1
## O5 25 0.31 0.0966 0.90 1
## E7 17 0.0720 0.93 1
## O4 24 0.0509 0.95 1
## A8 8 0.0502 0.95 1
## E9 19 0.0413 0.96 1
## A10 10 0.0348 0.97 1
## O8 28 0.0305 0.97 1
## O10 30 0.0186 0.98 1
## O1 21 0.0163 0.98 1
## O6 26 0.0154 0.98 1
## E10 20 0.0104 0.99 1
## O9 29 0.0061 0.99 1
## O7 27 0.0034 1.00 1
##
## PC1
## SS loadings 5.44
## Proportion Var 0.18
##
## Mean item complexity = 1
## Test of the hypothesis that 1 component is sufficient.
##
## The root mean square of the residuals (RMSR) is 0.14
##
## Fit based upon off diagonal values = 0.55cat("\n\n ******* Output the communalities ******* \n")##
##
## ******* Output the communalities *******facsolrot$communality## A1 A2 A3 A4 A5 A6
## 0.386687010 0.515847746 0.295663588 0.293371005 0.432702074 0.419993950
## A7 A8 A9 A10 E1 E2
## 0.242941300 0.050193955 0.217242280 0.034755901 0.412047325 0.302635971
## E3 E4 E5 E6 E7 E8
## 0.264411435 0.296835660 0.396683708 0.143623073 0.072029014 0.130219036
## E9 E10 O1 O2 O3 O4
## 0.041313525 0.010434195 0.016308453 0.129850178 0.114569834 0.050888852
## O5 O6 O7 O8 O9 O10
## 0.096634425 0.015381110 0.003390273 0.030487130 0.006130375 0.018626437Step 8: Reliability Analysis
## Warning in psych::alpha(agree_a, check.keys = TRUE): Some items were negatively correlated with total scale and were automatically reversed.
## This is indicated by a negative sign for the variable name.##
## Reliability analysis
## Call: psych::alpha(x = agree_a, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.8 0.81 0.82 0.3 4.2 0.015 3.4 0.61 0.28
##
## lower alpha upper 95% confidence boundaries
## 0.78 0.8 0.83
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## A1 0.77 0.78 0.78 0.28 3.6 0.017 0.012 0.28
## A2 0.78 0.78 0.79 0.29 3.6 0.017 0.012 0.28
## A3 0.78 0.78 0.79 0.29 3.6 0.017 0.012 0.28
## A4 0.78 0.79 0.79 0.29 3.7 0.017 0.016 0.28
## A5 0.78 0.79 0.79 0.29 3.7 0.017 0.015 0.28
## A6 0.78 0.79 0.79 0.29 3.7 0.017 0.011 0.28
## A7 0.79 0.79 0.80 0.30 3.8 0.016 0.017 0.30
## A8- 0.81 0.81 0.81 0.32 4.3 0.015 0.013 0.31
## A9- 0.79 0.79 0.80 0.30 3.8 0.016 0.017 0.28
## A10- 0.81 0.81 0.82 0.33 4.4 0.015 0.011 0.31
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## A1 382 0.70 0.69 0.66 0.59 3.7 1.13
## A2 382 0.66 0.67 0.63 0.55 3.9 1.00
## A3 382 0.67 0.66 0.63 0.55 3.8 1.08
## A4 382 0.64 0.63 0.58 0.52 3.8 1.02
## A5 382 0.63 0.64 0.59 0.53 3.9 0.87
## A6 382 0.63 0.64 0.60 0.53 3.7 0.92
## A7 382 0.59 0.61 0.54 0.49 3.9 0.87
## A8- 382 0.49 0.47 0.36 0.32 2.0 1.16
## A9- 382 0.62 0.62 0.56 0.50 3.0 0.98
## A10- 382 0.43 0.43 0.32 0.28 2.6 1.05
##
## Non missing response frequency for each item
## 0 1 2 3 4 5 miss
## A1 0.01 0.03 0.12 0.14 0.47 0.23 0
## A2 0.01 0.02 0.06 0.18 0.48 0.26 0
## A3 0.01 0.03 0.08 0.15 0.47 0.25 0
## A4 0.01 0.02 0.08 0.17 0.51 0.20 0
## A5 0.00 0.01 0.05 0.17 0.52 0.25 0
## A6 0.01 0.02 0.05 0.25 0.49 0.18 0
## A7 0.00 0.01 0.07 0.10 0.59 0.22 0
## A8 0.01 0.07 0.30 0.26 0.25 0.10 0
## A9 0.02 0.31 0.43 0.15 0.08 0.01 0
## A10 0.01 0.17 0.43 0.21 0.15 0.03 0## Warning in psych::alpha(extra_e, check.keys = TRUE): Some items were negatively correlated with total scale and were automatically reversed.
## This is indicated by a negative sign for the variable name.##
## Reliability analysis
## Call: psych::alpha(x = extra_e, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.76 0.75 0.79 0.23 3.1 0.018 2.9 0.65 0.2
##
## lower alpha upper 95% confidence boundaries
## 0.72 0.76 0.79
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## E1 0.71 0.71 0.75 0.21 2.4 0.022 0.030 0.20
## E2 0.71 0.71 0.75 0.21 2.4 0.022 0.025 0.17
## E3 0.74 0.73 0.76 0.23 2.6 0.020 0.033 0.20
## E4 0.71 0.71 0.75 0.21 2.4 0.022 0.028 0.17
## E5 0.74 0.73 0.77 0.23 2.7 0.019 0.035 0.18
## E6 0.74 0.74 0.78 0.24 2.8 0.019 0.035 0.20
## E7- 0.76 0.75 0.79 0.25 3.1 0.018 0.035 0.24
## E8- 0.73 0.73 0.76 0.23 2.7 0.020 0.032 0.21
## E9- 0.77 0.77 0.80 0.27 3.3 0.017 0.033 0.27
## E10- 0.77 0.76 0.80 0.26 3.2 0.017 0.034 0.27
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## E1 382 0.71 0.70 0.67 0.60 2.6 1.17
## E2 382 0.73 0.70 0.70 0.61 2.9 1.33
## E3 382 0.58 0.61 0.57 0.46 3.9 1.04
## E4 382 0.74 0.71 0.70 0.63 2.7 1.25
## E5 382 0.55 0.58 0.53 0.43 3.9 0.95
## E6 382 0.57 0.55 0.47 0.41 2.8 1.30
## E7- 382 0.41 0.43 0.34 0.25 2.9 1.11
## E8- 382 0.62 0.59 0.55 0.48 1.9 1.25
## E9- 382 0.30 0.34 0.21 0.16 3.0 1.01
## E10- 382 0.38 0.37 0.23 0.21 2.7 1.17
##
## Non missing response frequency for each item
## 0 1 2 3 4 5 miss
## E1 0.01 0.20 0.31 0.27 0.15 0.06 0
## E2 0.01 0.16 0.23 0.19 0.28 0.13 0
## E3 0.01 0.02 0.07 0.15 0.45 0.31 0
## E4 0.01 0.20 0.27 0.21 0.24 0.07 0
## E5 0.02 0.01 0.04 0.13 0.54 0.25 0
## E6 0.01 0.16 0.29 0.20 0.22 0.12 0
## E7 0.01 0.35 0.37 0.12 0.12 0.03 0
## E8 0.01 0.08 0.28 0.22 0.25 0.16 0
## E9 0.01 0.29 0.46 0.14 0.07 0.03 0
## E10 0.01 0.27 0.39 0.15 0.12 0.05 0## Warning in psych::alpha(open_o, check.keys = TRUE): Some items were negatively correlated with total scale and were automatically reversed.
## This is indicated by a negative sign for the variable name.##
## Reliability analysis
## Call: psych::alpha(x = open_o, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.79 0.78 0.81 0.27 3.6 0.016 2.3 0.69 0.26
##
## lower alpha upper 95% confidence boundaries
## 0.76 0.79 0.82
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## O1- 0.80 0.79 0.81 0.30 3.9 0.015 0.018 0.27
## O2- 0.76 0.76 0.79 0.26 3.1 0.018 0.026 0.23
## O3- 0.77 0.77 0.80 0.27 3.3 0.017 0.027 0.25
## O4- 0.77 0.76 0.78 0.26 3.2 0.017 0.026 0.26
## O5- 0.77 0.77 0.79 0.27 3.3 0.017 0.025 0.26
## O6 0.77 0.77 0.79 0.27 3.3 0.018 0.025 0.27
## O7 0.76 0.76 0.78 0.26 3.1 0.018 0.025 0.25
## O8 0.75 0.75 0.77 0.25 3.0 0.019 0.020 0.25
## O9 0.76 0.76 0.78 0.26 3.1 0.018 0.022 0.25
## O10 0.78 0.77 0.80 0.28 3.4 0.017 0.021 0.25
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## O1- 382 0.35 0.38 0.27 0.20 1.4 1.08
## O2- 382 0.64 0.64 0.58 0.52 2.2 1.21
## O3- 382 0.54 0.57 0.49 0.42 1.4 1.02
## O4- 382 0.59 0.61 0.56 0.46 1.5 1.12
## O5- 382 0.53 0.57 0.51 0.42 1.4 0.99
## O6 382 0.60 0.58 0.51 0.46 3.0 1.25
## O7 382 0.65 0.64 0.59 0.53 2.9 1.20
## O8 382 0.73 0.70 0.69 0.62 3.1 1.35
## O9 382 0.66 0.63 0.59 0.53 3.1 1.30
## O10 382 0.54 0.52 0.45 0.40 3.5 1.17
##
## Non missing response frequency for each item
## 0 1 2 3 4 5 miss
## O1 0.02 0.01 0.14 0.18 0.47 0.19 0
## O2 0.01 0.15 0.30 0.21 0.25 0.07 0
## O3 0.01 0.03 0.10 0.20 0.52 0.13 0
## O4 0.01 0.04 0.15 0.26 0.37 0.18 0
## O5 0.01 0.02 0.10 0.25 0.46 0.15 0
## O6 0.02 0.11 0.27 0.19 0.31 0.10 0
## O7 0.01 0.12 0.33 0.18 0.29 0.07 0
## O8 0.01 0.13 0.21 0.16 0.31 0.17 0
## O9 0.01 0.12 0.25 0.15 0.34 0.13 0
## O10 0.01 0.05 0.16 0.14 0.47 0.17 0report: A,E,O three Types of Items
A principal component analysis (PCA) was conducted on the 30 items with orthogonal rotation (varimax). Bartlett’s test of sphericity, Χ2(435) = 3978.985, p< .001, indicated that correlations between items were sufficiently large for PCA. An initial analysis was run to obtain eigenvalues for each component in the data. Four components had eigenvalues over Kaiser’s criterion of 1 and in combination explained 50.94% of the variance. The scree plot was slightly ambiguous and showed inflexions that would justify retaining either 3 or 5 factors.
Given the large sample size, and the convergence of the scree plot and Kaiser’s criterion on three components, three components were retained in the final analysis. component 1 represents agreeableness , component 2 extraversion and component 3 openness.
The aggrement component subscales of the RAQ had high reliability, Cronbach’s α = 0.80; the openess subscales of the RAQ had great reliability, Cronbach’s α = 0.79. The extraversion of statistics do not achieve a reliability of Cronbach’s α = 0.76, refer to Goldberg LR, Johnson JA, Eber HW, et al (2006) .